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Chapter 12Resource Masters
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Permission isgranted to reproduce the material contained herein on the condition that suchmaterial be reproduced only for classroom use; be provided to students, teachers,and families without charge; and be used solely in conjunction with GlencoeCalifornia Mathematics, Grade 6. Any other reproduction, for use or sale, isprohibited without prior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240
ISBN: 978-0-07-878307-4MHID: 0-07-878307-0 CAGR6 CRM12
Printed in the United States of America
4 5 6 7 8 9 10 MAL 14 13 12 11 10 09
Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters
booklets are available as consumable workbooks in both English and Spanish.
MHID ISBNStudy Guide and Intervention Workbook 0-07-878871-4 978-0-07-878871-0
Skills Practice Workbook 0-07-878873-0 978-0-07-878873-4
Practice Workbook 0-07-878875-7 978-0-07-878875-8
Word Problem Practice Workbook 0-07-878877-3 978-0-07-878877-2
Spanish VersionsStudy Guide and Intervention Workbook 0-07-878872-2 978-0-07-878872-7Skills Practice Workbook 0-07-878874-9 978-0-07-878874-1Practice Workbook 0-07-878876-5 978-0-07-878876-5Word Problem Practice Workbook 0-07-878878-1 978-0-07-878878-9
Answers for Workbooks The answers for Chapter 12 of these workbooks can be found in the
back of this Chapter Resource Masters booklet.
StudentWorks Plus™ This CD-ROM includes the entire Student Edition test along with the
English workbooks listed above.
TeacherWorks Plus™ All of the materials found in this booklet are included for viewing,
printing, and editing in this CD-ROM.
Spanish Assessment Masters MHID: 0-07-878879-X ISBN: 978-0-07-878879-6
These masters contain a Spanish version of Chapter 12 Test Form 2A and Form 2C.
iii
Teacher’s Guide to Using the Chapter 12 Resource Masters .........................................iv
Chapter Resources Chapter 12 Student-Built Glossary ....................1Chapter 12 Family Letter (English) ....................3Chapter 12 Family Activity (English) ..................4Chapter 12 Family Letter (Spanish) ...................5Chapter 12 Family Activity (Spanish).................6Chapter 12 Anticipation Guide (English)............7Chapter 12 Anticipation Guide (Spanish) ..........8
Lesson 12-1 Estimating SquareRootsLesson Reading Guide ......................................9Study Guide and Intervention ..........................10Skills Practice...................................................11Practice ............................................................12Word Problem Practice ....................................13Enrichment .......................................................14Scientific Calculator Activity .............................15
Lesson 12-2 The PythagoreanTheoremLesson Reading Guide ....................................16Study Guide and Intervention ..........................17Skills Practice...................................................18Practice ............................................................19Word Problem Practice ....................................20Enrichment .......................................................21
Lesson 12-3 Problem-SolvingInvestigation: Make a ModelStudy Guide and Intervention ..........................22Skills Practice...................................................23Practice ............................................................24Word Problem Practice ....................................25
Lesson 12-4 Surface Area ofRectangular PrismsLesson Reading Guide ....................................26Study Guide and Intervention ..........................27Skills Practice...................................................28Practice ............................................................29Word Problem Practice ....................................30Enrichment .......................................................31
Lesson 12-5 Surface Area ofCylindersLesson Reading Guide ....................................32Study Guide and Intervention ..........................33Skills Practice...................................................34Practice ............................................................35Word Problem Practice ....................................36Enrichment .......................................................37Scientific Calculator Activity .............................38
Chapter 12 AssessmentStudent Recording Sheet for Standardized
Test Practice ................................................39Rubric for Scoring Pre-AP................................40Chapter 12 Quizzes 1 and 2 ............................41Chapter 12 Quizzes 3 and 4 ............................42Chapter 12 Mid-Chapter Test ...........................43Chapter 12 Vocabulary Test .............................44Chapter 12 Test, Form 1 ..................................45Chapter 12 Test, Form 2A................................47Chapter 12 Test, Form 2B................................49Chapter 12 Test, Form 2C................................51Chapter 12 Test, Form 2D................................53Chapter 12 Test, Form 3 ..................................55Chapter 12 Extended-Response Test ..............57Chapter 12 Standardized Test Practice............58Unit 5 Test ........................................................61
Answers..................................................A1–A27
Contents
iv
Teacher’s Guide to Using the Chapter 12 Resource Masters
The Chapter 12 Resource Masters includes the core materials needed for Chapter 12. Thesematerials include worksheets, extensions, and assessment options. The answers for thesepages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing on theTeacherWorks Plus™ CD-ROM.
Chapter ResourcesStudent-Built Glossary (page 1) Thesemasters are a student study tool thatpresents up to twenty of the key vocabularyterms from the chapter. Students are torecord definitions and/or examples for eachterm. You may suggest that studentshighlight or star the terms with which theyare not familiar. Give this to students beforebeginning Lesson 12-1. Encourage them toadd these pages to their mathematics studynotebooks. Remind them to complete theappropriate words as they study each lesson.
Family Letter and Family Activity(pages 3–6) The letter informs yourstudents’ families of the mathematics theywill be learning in this chapter. The familyactivity helps them to practice problems thatare similar to those on the state test. A fullsolution for each problem is included.Spanish versions of these pages are alsoincluded. Give these to students to takehome before beginning the chapter.
Anticipation Guide (pages 7–8) Thismaster, presented in both English andSpanish, is a survey used before beginningthe chapter to pinpoint what students mayor may not know about the concepts in thechapter. Students will revisit this surveyafter they complete the chapter to see iftheir perceptions have changed.
Lesson ResourcesLesson Reading Guide Get Ready for theLesson reiterates the questions from thebeginning of the Student Edition lesson.Read the Lesson asks students to interpretthe context of and relationships amongterms in the lesson. Finally, RememberWhat You Learned asks students tosummarize what they have learned usingvarious representation techniques. Use as astudy tool for note taking or as an informalreading assignment. It is also a helpful toolfor ELL (English Language Learners).
Study Guide and Intervention Thismaster provides vocabulary, key concepts,additional worked-out examples and CheckYour Progress exercises to use as areteaching activity. It can also be used inconjunction with the Student Edition as aninstructional tool for students who havebeen absent.
Skills Practice This master focuses moreon the computational nature of the lesson.Use as an additional practice option or ashomework for second-day teaching of thelesson.
Practice This master closely follows thetypes of problems found in the Exercisessection of the Student Edition and includesword problems. Use as an additionalpractice option or as homework for second-day teaching of the lesson.
v
Word Problem Practice This masterincludes additional practice in solving wordproblems that apply the concepts of thelesson. Use as an additional practice or ashomework for second-day teaching of thelesson.
Enrichment These activities may extendthe concepts of the lesson, offer an historicalor multicultural look at the concepts, orwiden students’ perspectives on themathematics they are learning. They arewritten for use with all levels of students.
Graphing Calculator, ScientificCalculator, or Spreadsheet ActivitiesThese activities present ways in whichtechnology can be used with the concepts insome lessons of this chapter. Use as analternative approach to some concepts or asan integral part of your lesson presentation.
Assessment OptionsThe assessment masters in the Chapter 12Resource Masters offer a wide range ofassessment tools for formative (monitoring)assessment and summative (final) assessment.
Student Recording Sheet This mastercorresponds with the standardized testpractice at the end of the chapter.
Pre-AP Rubric This master providesinformation for teachers and students onhow to assess performance on open-endedquestions.
Quizzes Four free-response quizzes offerassessment at appropriate intervals in thechapter.
Mid-Chapter Test This 1-page testprovides an option to assess the first half ofthe chapter. It parallels the timing of theMid-Chapter Quiz in the Student Editionand includes both multiple-choice and free-response questions.
Vocabulary Test This test is suitable forall students. It includes a list of vocabularywords and 10 questions to assess students’knowledge of those words. This can also beused in conjunction with one of the leveledchapter tests.
Leveled Chapter Tests• Form 1 contains multiple-choice questions
and is intended for use with below gradelevel students.
• Forms 2A and 2B contain multiple-choicequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D contain free-responsequestions aimed at on grade levelstudents. These tests are similar in formatto offer comparable testing situations.
• Form 3 is a free-response test for use withabove grade level students.
All of the above mentioned tests include afree-response Bonus question.
Extended-Response Test Performanceassessment tasks are suitable for allstudents. Sample answers and a scoringrubric are included for evaluation.
Standardized Test Practice These threepages are cumulative in nature. It includesthree parts: multiple-choice questions withbubble-in answer format, griddablequestions with answer grids, and short-answer free-response questions.
Answers• The answers for the Anticipation Guide
and Lesson Resources are provided asreduced pages with answers appearing in red.
• Full-size answer keys are provided for theassessment masters.
Chapter 12 1 Glencoe California Mathematics, Grade 6
Vocabulary TermFound
Definition/Description/Exampleon Page
hypotenuse
irrational number
leg
Pythagorean Theorem
surface area
NAME ________________________________________ DATE ______________ PERIOD _____
Student-Built Glossary
Ch
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esThis is an alphabetical list of new vocabulary terms you will learn inChapter 12. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add this page to your math study notebook to reviewvocabulary at the end of the chapter.
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Family LetterNAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 3 Glencoe California Mathematics, Grade 6
Dear Parent or Guardian:
We use math skills in many of the things that we do. One of
the goals of this class is to show students how things they are
learning in the classroom are relevant to the real world. For
example, understanding the Pythagorean Theorem and surface
area geography, navigation, sports, and architecture.
In Chapter 12, Extending Geometry and Measurement, your
child will learn how to find squares and square roots, use the
Pythagorean Theorem, and find surface areas of rectangular
prisms and cylinders. In the study of this chapter, your child will
complete a variety of daily classroom assignments and activities
and possibly produce a chapter project.
By signing this letter and returning it with your child, you agree
to encourage your child by getting involved. Enclosed is an
activity you can do with your child that practices how the math
in Chapter 12 might be tested. You may also wish to log on to
ca.gr6math.com for self-check quizzes and other study help.
If you have any questions or comments, feel free to contact me
at school.Sincerely,
Signature of Parent or Guardian ______________________________________ Date ________
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Family ActivityStandards Practice
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 4 Glencoe California Mathematics, Grade 6
1. Andy is flying a kite as shown in thediagram.
What is the height of the kite?
A 4 feet B 8 feet C 12 feet D 16 feet
Fold here.
Solution
1. Hint: The Pythagorean Theorem statesthat the sum of the squares of the legs ofa right triangle is equal to the square ofthe hypotenuse, or a2 � b2 � c2.
The height of the kite is a leg of a righttriangle.
h2 � 62 � 102
h2 � 36 � 100h2 � 64h � 8
The answer is B.
2. Polly is painting all sides of the woodenblock shown below as the first step in anart project.
Which of the following will help hercalculate how much paint to buy?
A the volume; 720 cubic inchesB the surface area; 504 square inchesC adding the perimeter of each face;
224 inchesD the sum of the edges; 112 inches
Solution
2. The paint will cover all of the outsidesurfaces of the box. The measurementthat corresponds with the area of all ofthe faces is the surface area, which iscalculated by adding the areas of all ofthe faces.
The answer is B.
12
Fold the page along the dashed line. Work each problem on another piece of paper.Then unfold the page to check your work.
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10 ft
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10 in.
12 in.6 in.
Carta a la familiaNOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Capítulo 12 5 Glencoe California Mathematics, Grade 6
Estimado padre o apoderado:
Usamos destrezas matemáticas en muchas de las cosas que
hacemos. Uno de los objetivos de esta clase es demostrar a los
alumnos lo relevante que resulta para el mundo real las cosas
que estudian en el aula. Por ejemplo, comprender el teorema de
Pitágoras, la geografía del área de superficie, navegación,
deportes y arquitectura.
En el Capítulo 12, Álgebra y geometría: Extensión, su hijo(a)
aprenderá a calcular cuadrados y raíces cuadradas, a usar el teo-
rema de Pitágoras y a calcular el área de superficie de prismas y
cilindros rectangulares. En el estudio de este capítulo, su hijo(a)
completará una variedad de tareas y actividades diarias y es posi-
ble que trabaje en un proyecto del capítulo.
Al firmar esta carta y devolverla con su hijo(a), usted se com-
promete a ayudarlo(a) a participar en su aprendizaje. Junto con
esta carta, va incluida una actividad que puede realizar con
él(ella) y la cual practica lo que podrían encontrar en las prue-
bas de los conceptos matemáticos que aprenderán en el
Capítulo 12. Además, visiten ca.gr6math.com para ver
autocontroles y otras ayudas para el estudio. Si tiene cualquier
pregunta o comentario, por favor contácteme en la escuela.
Cordialmente,
Firma del padre o apoderado ________________________________________ Fecha ______
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Actividad en familiaPráctica de estándares
NOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Capítulo 12 6 Glencoe California Mathematics, Grade 6
1. Andy vuela una cometa como se mues-tra en el diagrama.
¿Cuál es la altura de la cometa?
A 4 pies B 8 pies C 12 pies D 16 pies
Doblen aquí.
Solución
1. H1. Ayuda: El teorema de Pitágorasestablece que la suma de los cuadradosde los catetos de un ángulo recto esigual al cuadrado de la hipotenusa ó a2 �b2 � c2.
La altura de la cometa es un cateto deun triángulo rectángulo.
h2 � 62 � 102
h2 � 36 � 100h2 � 64h � 8
La respuesta es B.
2. Polly pinta todos los lados de un bloquede madera como primer paso de unproyecto artístico.
¿Cuál de los siguientes le ayudará acalcular cuánta pintura debe comprar?
A el volumen; 720 pulgadas cúbicasB el área de superficie; 504 pulgadas
cuadradasC sumar el perímetro de cada cara;
224 pulgadasD la suma de las aristas; 112 pulgadas
Solución
2. La pintura cubrirá toda la superficieexterna del bloque. La medida quecorresponde al área de todas las carases el área de superficie, la cual secalcula sumando las áreas de todas lascaras.
La respuesta es B.
10 pulg
12 pulg6 pulg
6 pies
10 pies
Groundpoint Andy
12
Doblen la página a lo largo de las líneas punteadas. Resuelvan cada problema en otra hoja de papel. Luego, desdoblen la página y revisen las respuestas.
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NAME ________________________________________ DATE ______________ PERIOD _____
Anticipation GuideExtending Algebra and Geometry
Chapter 12 7 Glencoe California Mathematics, Grade 6
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Step 2
Step 1
STEP 1 Statement STEP 2A, D, or NS A or D
1. A square root of a number is one of its two equal factors.2. You can find an estimate for the square root of 45 by finding
the square root of the perfect square closest to 45.3. All square roots are irrational numbers.4. The hypotenuse of a right triangle is the side opposite the
right angle.5. Since 102 � 62 � 82, a triangle whose sides have lengths 6,
8, and 10 will be a right triangle.6. Since a rectangular prism has six sides, the surface area
can be found by finding the area of one side and multiplying by 6.
7. If the dimensions of a rectangular prism are doubled, the surface area will also double.
8. If the dimensions of a rectangular prism are doubled, the volume will triple.
9. In finding the surface area of a cylinder, you are finding the area of two circles and a rectangle.
10. The units for surface area are always cubic units since surface area involves three-dimensional figures.
Before you begin Chapter 12
• Read each statement.
• Decide whether you Agree (A) or Disagree (D) with the statement.
• Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure).
After you complete Chapter 12
• Reread each statement and complete the last column by entering an A or a D.
• Did any of your opinions about the statements change from the first column?
• For those statements that you mark with a D, use a piece of paper to write an example of why you disagree.
12
NOMBRE ______________________________________ FECHA ____________ PERÍODO ___
Ejercicios preparatoriosÁlgebra y geometría: Extensión
Capítulo 12 8 Glencoe California Mathematics, Grade 6
Copyright ©
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PASO 2
Antes de comenzar el Capítulo 12
• Lee cada enunciado.
• Decide si estás de acuerdo (A) o en desacuerdo (D) con el enunciado.
• Escribe A o D en la primera columna O si no estás seguro(a) de la respuesta,escribe NS (No estoy seguro(a).
Después de completar el Capítulo 12
• Vuelve a leer cada enunciado y completa la última columna con una A o una D.
• ¿Cambió cualquiera de tus opiniones sobre los enunciados de la primera columna?
• En una hoja de papel aparte, escribe un ejemplo de por qué estás en desacuerdo con losenunciados que marcaste con una D.
PASO 1
PASO 1 PASO 2A, D o NS
EnunciadoA o D
1. Una raíz cuadrada de un número es uno de sus dos factores iguales.
2. Puedes estimar la raíz cuadrada de 45 al extraer la raíz del cuadrado perfecto más cercano a 45.
3. Todas las raíces cuadradas son números irracionales.4. La hipotenusa de un triángulo rectángulo es el lado opuesto
al ángulo recto.5. Dado que 102 � 62 � 82, un triángulo con lados de 6, 8 y 10
será un triángulo rectángulo.6. Dado que un prisma rectangular tiene seis lados, el área de
superficie se puede hallar calculando el área de un lado y multiplicándola por 6.
7. Si se duplican las dimensiones de un prisma rectangular,también se duplicará el área de superficie.
8. Si se duplican las dimensiones de un prisma rectangular, el volumen se triplicará.
9. Al calcular el área de superficie de un cilindro, estás calculando las áreas de dos círculos y un rectángulo.
10. Las unidades para el área de superficie son siempre cúbicas,dado que el área de superficie incluye figuras tridimensionales.
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Chapter 12 9 Glencoe California Mathematics, Grade 6
Get Ready for the LessonComplete the Mini Lab at the top of page 636 in your textbook. Writeyour answers below. Use algebra tiles to estimate the square root ofeach number to the nearest whole number.
1. 40 2. 28 3. 85 4. 62
5. Describe another method that you could use to estimate the square rootof a number.
Read the Lesson
6. Why is �4� a rational number and �2� an irrational number?
7. How do you read the statement �64� � �75� � �81�?
8. Why are �64� and �81� used in Example 1?
Remember What You Learned9. The key to estimating square roots without a calculator is to be familiar
with common perfect squares. Complete the following table of commonperfect squares then test yourself to see how many you can rememberwithout using a calculator.
Number 5 6 7 8 9 10 11 12 13 14 15 16 20 25
Square 25
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading GuideEstimating Square Roots
12-1 7NS2.4
Exercises
Example 2
Example 1
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionEstimating Square Roots
Chapter 12 10 Glencoe California Mathematics, Grade 6
Copyright ©
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Estimate �40� to the nearest whole number.
List some perfect squares.
1, 4, 9, 16, 25, 36, 49, …
36 � 40 � 49 40 is between the perfect squares 36 and 49.
�36� � �40� � �49� Find the square root of each number.
6 � �40� � 7 �36� � 6 and �49� � 7
So, �40� is between 6 and 7. Since 40 is closer to 36 than to 49, the best whole numberestimate is 6.
Use a calculator to find the value of �28� tothe nearest tenth.
28 5.291502622
�28� � 5.3
Check Since 52 � 25 and 25 is close to 28, the answer is reasonable.
Estimate each square root to the nearest whole number.
1. �3� 2. �8�
3. �26� 4. �41�
5. �61� 6. �94�
7. �152� 8. �850�
Use a calculator to find each square root to the nearest tenth.
9. �2� 10. �27�
11. �73� 12. �82�
13. �105� 14. �395�
15. �846� 16. �2,298�
ENTER2nd
Recall that a perfect square is a square of a rational number. In Lesson 5-8, you learned that anynumber that can be written as a fraction is a rational number. A number that cannot be written as afraction is an irrational number.
0 1 2 3 4 5 6
28
7NS2.4
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeEstimating Square Roots
Chapter 12 11 Glencoe California Mathematics, Grade 6
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Estimate each square root to the nearest whole number.
1. �5� 2. �10� 3. �21�
4. �28� 5. �78� 6. �102�
7. �179� 8. �274� 9. �303�
10. �563� 11. �592� 12. �755�
13. �981� 14. �1,356� 15. �1,688�
16. �3,287� 17. �3,985� 18. �4,125�
Use a calculator to find each square root to the nearest tenth.
19. �6� 20. �19� 21. �30�
22. �77� 23. �114� 24. �125�
25. �149� 26. �182� 27. �212�
28. �436� 29. �621� 30. �853�
31. �918� 32. �1,004� 33. �1,270�
34. �5,438� 35. �4,215� 36. �5,786�
37. Order �275�, 4.91, and �23� from least to greatest.
38. Graph �42� and �62� on the same number line.
0 1 2 3 4 5 876
7NS2.4
Estimate each square root to the nearest whole number.
1. �8� 2. �19� 3. �47� 4. �70�
5. �91� 6. �125� 7. �150� 8. �389�
9. �2,468� 10. �899� 11. �4,840� 12. �8,080�
Use a calculator to find each square root to the nearest tenth.
13. �6� 14. �21� 15. �53� 16. �79�
17. �190� 18. �624� 19. �427� 20. �3,178�
21. �0.36� 22. �0.81� 23. �1.44� 24. �2.25�
25. ALGEBRA What whole number is closest to �a � b� if a � 24 and b � 38?
26. ALGEBRA Evaluate �x � y� to the nearest tenth if x � 10 and y � 4.5
27. QUILTING A queen-size quilt in the shape of a square has an area of 51square feet. What is the approximate length of one side of the quilt to thenearest tenth?
28. PENDULUM The formula below can be used to estimate the time it takesfor a pendulum to swing back and forth once. Use the formula to find thetime it takes for a pendulum with a length of 0.8 meter to swing back andforth once. Round to the nearest tenth.
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeEstimating Square Roots
Chapter 12 12 Glencoe California Mathematics, Grade 6
Copyright ©
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12-1
T � 2 � �L�• T � time (seconds)• L � length (meters)
7NS2.4
NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeEstimating Square Roots
Chapter 12 13 Glencoe California Mathematics, Grade 6
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1. GEOMETRY The diameter d of a circlewith area A is given by the formula
d � ��4�A��. What is the diameter of a
circle with an area of 56 square inches?Use 3.14 for � and round to the nearesttenth.
2. FENCING Carmen wants to buy fencingto enclose a square garden with anarea of 500 square feet. How muchfencing does Carmen need to buy?Round to the nearest tenth.
3. OCEANS The speed v in feet per secondof an ocean wave in shallow water ofdepth d in feet is given by the formulav � �32d�. What is the speed of anocean wave at a depth of 10 feet?Round to the nearest tenth.
4. LIGHTING A new flashlight has a beamwhose width w at a distance d from theflashlight is given by the formulaw � 1.2�d�. What is the width of thebeam at a distance of 30 feet? Round tothe nearest tenth.
5. SOUND The speed of sound in air c inmeters per second at a temperature Tin degrees Celsius is givenapproximately by the formula c � �402(T�� 273�)�. What is the speedof sound in air at a temperature of 25 degrees Celsius? Round to thenearest tenth.
6. PROJECTILES The muzzle velocity v infeet per second necessary for a cannonto hit a target x feet away is estimatedby the formula v � �32x�. What muzzlevelocity is required to hit a target3,000 feet away? Round to the nearesttenth.
3,000 ft
7NS2.4
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 12 14 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
12-1
World Series RecordsEach problem gives the name of a famous baseball player. To findwho set each record, graph the points on the number line.
1. pitched 23 strikeouts in one World Series
U at �3�, X at 3.3, K at 0.75, O at �32�, F at �6�, A at 2�
78�
2. 71 base hits in his appearances in World Series
B at �5�, R at �12�, A at 3.75, G at �1163�
, E at �52�, Y at 0.375, R at �
143�,
I at 1.6, and O at 0.7�
3. 10 runs in a single World Series
N at �60�, K at �30�, A at 4.3, S at 6.2, C at �496�, O at �45�, and J at �17�
4. batting average of 0.625 in a single World Series
E at �32�, U at 6�56�, A at �
134�, T at �55�, B at 5.3, R at �40�, H at 7.75,
B at �251�
5. 42 World Series runs in his career
E at �140�, Y at 9.6, I at 8.6, E at �90�, A at �221�, M at �70�, C at 8�
78�,
M at �100�, N at 10.7, K at 9�111�
, T at �120�, L at 11.4
0 4321
4 8765
0 4321
4 8765
8 1211109
7NS2.4
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Scientific Calculator ActivityEstimating Square Roots
Chapter 12 15 Glencoe California Mathematics, Grade 6
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A scientific calculator can be used to estimate square roots. On the TI-34 II, the square rootfunction is used by pressing the [��] keys.
Estimate �1�5�. Round to the nearest hundredth.
Enter: [��] 15 3.872983346
So, �1�5� � 3.87.
Estimate �2�2�. Round to the nearest hundredth.
Enter: [��] 22 4.69041576
So, �2�2� � 4.69.
Estimate �1�2�5�. Round to the nearest hundredth.
Enter: [��] 125 11.18033989
So, �1�2�5� � 11.18.
Use a calculator to estimate each square root. Round to the nearest hundredth.
1. �3�5� 2. �4�2� 3. �3�1�
4. �1�2�6� 5. �1�9�0� 6. �2�
7. �3� 8. �8� 9. �1�3�
10. �5�0� 11. �6�8� 12. �5�7�
13. �3�7� 14. �9�8� 15. �4�4�
16. �8�7� 17. �1�5� 18. �1�1�
19. �1�2� 20. �1�4� 21. �2�6�
ENTER
�)2nd
ENTER
�)2nd
ENTER
�)2nd
2nd
Example 2
Example 1
Example 3
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide The Pythagorean Theorem
Chapter 12 16 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
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panies, Inc.
12-2
Get Ready for the LessonRead the introduction at the top of page 640 in your textbook. Writeyour answers below.
1. Find the area of each square.
2. How are the squares of the sides related to the areas of the squares?
3. Find the sum of the areas of the two smaller squares. How does the sumcompare to the area of the larger square?
4. Use grid paper to cut out three squares with sides 5, 12, and 13 units. Form aright triangle with these squares. Compare the sum of the areas of the twosmaller squares with the area of the larger square.
Read the Lesson5. What does the symbol �� indicate?
6. How can you find the hypotenuse of a right triangle within a rectanglewhen given only the dimensions of the rectangle?
7. In Examples 3 and 4 on page 680, how do you know which length is c?
Remember What You Learned8. Summarize what you learned in this lesson by labeling the sides of the
right triangle with the letters a, b, and c and then completing the table.
You canfind
If you knowthe lengths
a
b
c
7MG3.3
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionThe Pythagorean Theorem
Chapter 12 17 Glencoe California Mathematics, Grade 6
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Find the missing measure of a right triangle if a � 4 inches and b � 3 inches.
c2 � a2 � b2 Pythagorean Theorem
c2 � 42 � 32 Replace a with 4 and b with 3.
c2 � 16 � 9 Evaluate 42 and 32.
c2 � 25 Add.
�c2� � �25� Take the positive square root of each side.
c � 5 Simplify.
The length of the hypotenuse is 5 inches.
Determine whether a triangle with side lengths of 6 meters,9 meters, and 12 meters is a right triangle.
c2 � a2 � b2 Pythagorean Theorem
122 � 62 � 92 Replace a with 6, b with 9, and c with 12.
144 � 36 � 81 Simplify.
144 117 Add.
The triangle is not a right triangle.
Find the missing measure of each right triangle. Round to the nearesttenth if necessary.
1. 2. 3.
Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.
4. 15 ft, 8 ft, 17 ft 5. 5 in., 13 in., 17 in. 6. 9 yd, 40 yd, 41 yd
13 cm
16 cm
a cm5 m
7.5 m
c m
9 in.
4 in.c in.
3 in.
4 in.c in.
The sides of a right triangle have special names. The sides adjacent to the right angle are the legs. The side opposite the right angle is the c2 � a2 � b2
hypotenuse. The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the lengths of the legs. In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.
b
ac
Example 1
Example 2
7MG3.3
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeThe Pythagorean Theorem
Chapter 12 18 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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-Hill, a division of T
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panies, Inc.
12-2
Find the missing measure of each right triangle. Round to the nearesttenth if necessary.
1. 2.
3. 4.
5. 6.
7. 8.
9. a � 15 cm, b � 20 cm 10. a � 2 yd, b � 12 yd
11. a � 13 in., c � 16.5 in. 12. b � 8 mm, c � 17 mm
13. a � 1.3 ft, b � 4.6 ft 14. a � 14.7 m, c � 23 m
Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.
15. 10 ft, 24 ft, 26 ft 16. 5 in., 8 in., 9 in.
17. 6 cm, 9 cm, 12 cm 18. 4.5 mm, 6.0 mm, 7.5 mm
14 mmc mm
6.7 mm
11.2 m
6 m
a m
2.7 yd 3 yd
a yd
20.3 in. 32 in.
c in.
20 cm
26 cmx cm12.4 ft
a ft
15 ft
5 in.
c in.
5 in.7 m
b m
20 m
7MG3.3
Find the missing measure of each triangle. Round to the nearesttenth if necessary.
1. 2. 3.
4. a � 3.3 in., b � 5.6 in. 5. b � 2.9 mm, c � 4.4 mm 6. a � 21 yd, c � 29 yd
7. a � 2�15
� ft, c � 4�25
�ft 8. b � 7�14
� in., c � 7�34
� in. 9. a � 6�12
� yd, b � 10 yd
If a triangle has sides a, b, and c so that a2 � b2 � c2, then the triangleis a right triangle. Determine whether a triangle with the given sidelengths is a right triangle. Write yes or no.
10. 9 cm, 12 cm, 18 cm 11. 7 ft, 24 ft, 25 ft 12. 5 in., 12 in., 13 in.
Find the missing measure in each figure. Round to the nearest tenthif necessary.
13. 14.
15. SOCCER Find the width of the soccer goal.Round to the nearest tenth.
16. CONVEYOR BELT The diagram shows thehorizontal distance a conveyor belt moves a load of gravel. If the conveyor belt takes54 seconds to move gravel from the bottomof the conveyor belt to the top at a rate of 3 feet per second, how high does theconveyor belt lift the gravel? Round to the nearest tenth.
150 ft
h ft
5 ft11.2 ft
x ft
2.5 yd
x yd
1.8 yd
30 m
x m9 m
18 m
4.7 m
6.1 ma m
24 ft23.8 ft
c ft
11 cm
7 cm c cm
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeThe Pythagorean Theorem
Chapter 12 19 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeThe Pythagorean Theorem
Chapter 12 20 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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12-2
1. ORIGAMI Chee has a piece of papermeasuring 8.5 inches by 8.5 inches. Ifshe folds the paper diagonally in half,how long is the folded side? Round tothe nearest tenth.
2. COMPUTERS In a computer catalog,a computer monitor is said to be 19 inches. This distance is the diagonaldistance across the screen. If the screenis 10 inches high, what is the width ofthe screen? Round to the nearest tenth.
3. ANTENNAS A wire 10 meters long issupporting a utility pole. The wire isanchored to the ground and is attachedto the pole 9 meters above the ground.What is the distance from the bottom ofthe pole to the point where the wire isattached to the ground? Round to thenearest tenth.
9 m10 m
x m
4. RAMPS Crystal wants to build a rampthat will rise 4 feet over a horizontaldistance of 20 feet. How long will theramp be? Round to the nearest tenth.
4 ft
20 ft
x ft
5. POOLS Salomon swims diagonallyacross his pool every day. If Salomon’spool is 4 meters wide and 16 metersdiagonally across, how long is his pool,to the nearest tenth of a meter?
6. FRAMES Rosa has a picture frame thatmeasures 12 inches by 18 inches. Whatis the diagonal distance across theframe? Round to the nearest tenth.
7MG3.3
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 12 21 Glencoe California Mathematics, Grade 6
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Pythagoras in the AirIn the diagram at the right, an airplane heads north at 180 mi/h.But, the wind is blowing towards the east at 30 mi/h. So, theairplane is really traveling east of north. The middle arrow in the diagram shows the actual direction of the airplane.
The actual speed of the plane can be found using the Pythagorean Theorem.
�302 �� 1802� � �900 �� 32,40�0�
� �33,30�0�
� 182.5
The plane’s actual speed is about 182.5 mi/h.
Find the actual speed of each airplane. Round answers to the nearesttenth. (You might wish to draw a diagram to help you solve theproblem.)
1. An airplane travels at 240 mi/h east. 2. An airplane travels at 620 mi/h west.A wind is blowing at 20 mi/h toward A wind is blowing at 35 mi/h towardthe south. the south.
3. An airplane travels at 450 mi/h south. 4. An airplane travels at 1,200 mi/h east.A wind is blowing at 40 mi/h toward A wind is blowing at 30 mi/h towardthe east. the north.
E
N(not drawn to scale)
180 mi/h
30 mi/h
7MG3.3
Exercises
Example
When solving problems, make a model to represent the given situation in order todetermine the best plan for a solution.
GIFT WRAP Rita wants to wrap a rectangular box. The box is 12 inches by 7 inches by 3 inches high. What must be the area
of the paper so that she has a 1 inch overlap to neatly wrap the paper?
1. GARDENING Peg wants to put a stone path 3 feet wide around herrectangular garden measuring 10 feet by 15 feet. What will be theperimeter of her garden including the stone path?
2. DRAWING Dante is making a full-size drawing of his favorite cartoon character. If the figure is 1 inch by 0.5 inches and his scale is 1 inch � 10 inches, how large will the full size character be?
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 22 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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12-3
Explore You know that the box is 12 � 7 � 3 and that you need to add 1 inch tosome measures for the overlap. You also know that the wrapping paper willbe a rectangle.
Plan Draw a sketch of the box and then make a model of the box if it were cutapart and laid flat. You need the overlap going around the box.
Solve Sketch the box. Make a model of the box unfolded.
The length of the paper needed is the distance around the box plus 1 inch. So, � � 7 � 3 � 7 � 3 � 1 or 21 inches.The width of the paper would be 3 � 12 � 3 or 18 inches.The area would be 21 � 18 or 378 in2.
Check Make a box using centimeters instead of inches. Then cut a piece of paper18 centimeters by 21 centimeters to see if you can wrap the box neatly.
�
bottom
frontsi
de
sidetop
back
1 in. overlap
7 in.
12 in.
3 in.
12 in.
7 in.
3 in.
6MR2.4, 6NS2.1Study Guide and InterventionProblem-Solving Investigation: Make a Model
Make a model to solve.
1. PETS Jack’s Pet Store has 5 pets for sale. Some are birds and some aredogs. When Jack looks at the pets, he counts 18 legs. How many of eachtype of pet are there?
2. INTERIOR DESIGN JoAnn is creating a model of a living room. The room is
20 feet by 20 feet. If the scale she is using is 1 foot � �12
� inch, what are the
dimensions of her model room?
3. ART COMPETITION An art competition allows for submitted work to be nolarger than 11 inches by 14 inches. If Christene’s photograph is 8 inchesby 10 inches, what is the largest matte she can use if she wants theborder to be the same width all the way around the photo?
4. FLOORING James is laying carpet in an L-shaped room whose model isshown below. How much carpet does he need?
5. SCALE MODEL Charlotte is building a model of the Eiffel Tower. If theactual tower is 986 feet tall and Charlotte’s scale is 1 inch � 10 feet, howtall is her model?
6. SCIENCE FAIR Audrey wants to make a poster that is folded into threesections for her science fair project. The length of the poster is 36 inches.If she wants the middle section to be twice the length of the side sectionsand she wants the two side sections to be equal, what should be thelength of the middle section?
8 ft
8 ft
8 ft
12 ft
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 23 Glencoe California Mathematics, Grade 6
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Problem-Solving Investigation: Make a Model
Mixed Problem Solving
Select the Operation
For Exercises 1 and 2, make a model tosolve the problem.
1. ARCHITECT Mrs. Peron is designing a home for a client. The house is 45 feet by 76 feet. If she uses a scale of 1 foot � �
12
� inch, what are the dimensions of the house on the blue prints?
2. SWIMMING POOL Mr. Forrester has a swimming pool that measures 3�
13
� yards by 8 yards. If the deck around the pool is 2�
23
� yards wide, what is the outside perimeter of the deck?
Use any strategy to solve Exercises 3and 4. Some strategies are shown below.
3. BATTERIES A manufacturing plant canmake 350 batteries in 15 minutes. Howlong will it take the manufacturingplant to make 3,500 batteries?
4. SHOPPING A grocery store has five cashregisters. About 4 customers arechecked out at each register every 20minutes. How many customers arechecked out at the store each hour?
For Exercises 5 and 6, select anappropriate operation(s) to solve theproblem. Justify your selection(s) andsolve the problem.
5. TESTS Diego scored a 95 on his first testin science class. He then scored 100 onhis next 5 tests. If he scored a 91 on hisseventh test, what is his test average?
6. NEWSPAPERS Candace wants to increasethe number of newspapers she delivers.She currently delivers 58 newspapers.In fourteen weeks, she wants to bedelivering 100 newspapers. How manynewspaper deliveries must she increaseeach week to obtain her goal?
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 24 Glencoe California Mathematics, Grade 6
Copyright ©
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-Hill, a division of T
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panies, Inc.
12-3
PROBLEM-SOLVING STRATEGIES
• Use the four-step plan.
• Draw a diagram.
• Use logical reasoning.
• Make a model.
6MR2.4, 6NS2.1PracticeProblem-Solving Investigation: Make a Model
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 25 Glencoe California Mathematics, Grade 6
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1. FOOTBALL Bill, Damon and Steve arethe quarterback, center and punter onthe football team, not necessarily inthat order. The quarterback and Bill goon the bus with Damon after the game.Damon is not the punter. What positiondoes Bill play?
2. SPORTS Janelle can walk one mile in 15 minutes. How long will it take her towalk 3 miles?
3. WEATHER The Loudonville Times printsthe following chart showing thesnowfall for each day last week. Thereporter estimates that they got 10inches of snow during the past week. Isthis a reasonable estimate?
4. GARDENING The table below shows howmany tomatoes Nicholas picked eachday during the week. How many doeshe need to pick on Sunday so that hehas picked a total of 20 for the week?
5. PAINT If one gallon of paint covers 150square feet, is one gallon enough forSusie to cover a kitchen wall that is 15feet by 8 feet? Justify your answer.
6. SHOPPING Avery bought a DVD for$22.99 and got $2.01 back in change.How much did Avery give the cashier?
7. MONEY The amount in Carly’scheckbook is $750 after writing a checkfor $65 and making a deposit of $100and a deposit of $75. How much did shestart with in her checkbook?
8. VEHICLES Jim has 15 vehicles at hisgarage. Some are cars and some aremotorcycles. If he counts 58 wheels,how many of each type of vehicle doeshe have?
Day SnowfallMonday 1 inchTuesday 2 inchesWednesday 0.5 inchesThursday 1.5 inchesFriday 3.75 inchesSaturday 0 inchesSunday 0 inches
Day M T W R F S S
Number of 2 5 3 1 0 5tomatoes
Solve each problem using any strategy you have learned.
6MR2.4, 6NS2.1Word Problem PracticeProblem-Solving Investigation: Make a Model
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 26 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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panies, Inc.
12-4
Get Ready for the LessonComplete the Mini Lab at the top of page 649 in your textbook. Writeyour answers below.
1. Record the dimensions,volume, and surface area in a table.
2. Build two more prisms using all of the cubes.For each, record the dimensions, volume,and surface area.
3. Describe the prisms with the greatest and least surface areas.
Read the Lesson4. How many pairs of congruent faces are there in a rectangular prism?
Name them.
5. Tell how to find the surface area of a rectangular prism in words.
Remember What You Learned6. Work with a partner. Bring a box that is a rectangular prism to class
(any size, such as a crayon box) that you can cut apart to form a net.Label the surfaces front, back, top, bottom, side, side. Measure the facesand find the surface area. Use adhesive tape to form the net into a three-dimensional figure. Then exchange nets with your partner. Calculate thevolume of the prism. Compare the answers found from using a net and asolid.
Dimensions Volume SurfaceArea
7MG2.1Lesson Reading Guide Surface Area of Rectangular Prisms
Exercises
Example
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 27 Glencoe California Mathematics, Grade 6
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Find the surface area of the rectangular prism.
You can use the net of the rectangular prism to find its surface area. There are three pairs of congruent faces in a rectangular prism:
� top and bottom� front and back� two sides
Faces Area
top and bottom (4 � 3) � (4 � 3) � 24
front and back (4 � 2) � (4 � 2) � 16
two sides (2 � 3) � (2 � 3) � 12
Sum of the areas 24 � 16 � 12 � 52
Alternatively, replace � with 4, w with 3, and h with 2 in the formula for surface area.S � 2�w � 2�h � 2wh
� 2 � 4 � 3 � 2 � 4 � 2 � 2 � 3 � 2 Follow order of operations.� 24 � 16 � 12 � 52
So, the surface area of the rectangular prism is 52 square meters.
Find the surface area of each rectangular prism.
1. 2. 3.
5 ft7 ft
9 ft
8 in.
10 in.2 in.3 cm
3 cm
7 cm
4 m
4 m
3 m
2 m
2 m
3 m
2 mback
side bottom side
front
top
4 m3 m
2 m
The sum of the areas of all the surfaces, or faces, of a three-dimensional figure is the surface area.The surface area S of a rectangular prism with length �, width w, and height h is found using the following formula.
S � 2�w � 2�h � 2wh
7MG2.1Study Guide and InterventionSurface Area of Rectangular Prisms
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 28 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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panies, Inc.
12-4
Find the surface area of each rectangular prism. Round to thenearest tenth if necessary.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. A cube has a surface area of 126 square feet. What is the area of oneface?
11. Find the surface area of a rectangular prism that has a length of 8 inches, a width of 3 inches, and a height of 6 inches.
6.4 mm
7.3 mm4.1 mm
4.5 in.
4.1 in.8.3 in.6 ft
12 ft
7 ft
4.3 in.
6 in.
3.7 in.
3 cm4 cm
8.5 cm10 mm
9 mm
9 mm
15 in.
9 in.7 in.
1 ft4 ft
7 ft
12 cm
7 cm
6 cm
7MG2.1Skills PracticeSurface Area of Rectangular Prisms
Find the surface area of each rectangular prism. Round to thenearest tenth if necessary.
1. 2. 3.
4. length � 20 cm 5. length � 31.5 in. 6. length � 5.3 mmwidth � 18 cm width � 12.2 in. width � 1.1 mmheight � 25 cm height � 24.8 in. height � 3.4 mm
7. 8.
ESTIMATION Estimate the surface area of each prism.
9. 10.
11. BIRTHDAY GIFT When wrapping a birthday gift for his mother, Kenji addsan additional 2.5 square feet of gift wrap to allow for overlap. How manysquare feet of gift wrap will Kenji use to wrap a gift 3.5 feet long,18 inches wide, and 2 feet high?
For Exercises 12 and 13, use the following information.
A company needs to package hazardous chemicals in special plastic containers that hold 80 cubic feet of chemicals.12. Find the whole number dimensions of the container that would use the
least amount of plastic.
13. If the plastic costs $0.10 per square foot, how much would it cost to make24 containers?
8.1 in.
3.8 in.
4.2 in.
8.9 mm8.9 mm
8.9 mm
x ft
7.3 ft
3 ft
4.8 ft
5 m3 m
2 m
x m
8 yd14
6 yd
12 yd
23
1.6 m
5.5 m
1.2 m
2 ft6 ft
3 ft
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 29 Glencoe California Mathematics, Grade 6
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Surface Area of Rectangular Prisms
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 30 Glencoe California Mathematics, Grade 6
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panies, Inc.
12-4
1. PACKAGING A packaging companyneeds to know how much cardboardwill be required to make boxes18 inches long, 12 inches wide, and10 inches high. How much cardboardwill be needed for each box if there isno overlap in the construction?
2. INSULATION Jane needs to buyinsulation for the inside of a truckcontainer. The container is arectangular prism 15 feet long, 8 feet
wide, and 7�12� feet high. How much
insulation should Jane buy if all insidesurfaces except the floor are to beinsulated?
3. ICE Suppose the length of each edge ofa cube of ice is 4 centimeters. Find thesurface area of the cube.
4 cm
4. ICE Suppose you cut the ice cube fromExercise 3 in half horizontally into twosmaller rectangular prisms. Find thesurface area of one of the two smallerprisms.
5. CONTAINERS What is the total surfacearea of the inside and outside of acontainer in the shape of a rectangularprism with length of 5 meters, width of3 meters, and height of 2.2 meters?
6. TOYS Oscar is making a play block forhis baby sister by gluing fabric over theentire surface of a foam block. Howmuch fabric will Oscar need?
6.1 in.2.3 in.
2.3 in.
7MG2.1Word Problem PracticeSurface Area of Rectangular Prisms
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 12 31 Glencoe California Mathematics, Grade 6
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Pattern Puzzles1. Make three copies of this
pattern. Fold each pattern to make a pyramid. Then, put the three pyramids together to make a cube. Draw a sketch of the completed cube.
2. Make four copies of this pattern.Fold each pattern to make a solid figure. Then, put the four solids together to make a pyramid. Make a sketch of the finished pyramid.
3. Find the surface area of the cube in Exercise 1.
7MG2.1
NAME ________________________________________ DATE ______________ PERIOD _____
Lesson Reading Guide Surface Area of Cylinders
Chapter 12 32 Glencoe California Mathematics, Grade 6
Copyright ©
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12-5
Get Ready for the LessonComplete the Mini Lab at the top of page 656 in your textbook. Writeyour answers below.
1. Make a net of the cylinder.
2. Name the shapes in the net.
3. How is the length of the rectangle related to the circles?
4. Explain how to find the surface area of the cylinder.
Read the LessonWrite the formula to use to find each of the following.
5. the area of a circle _______________
6. the circumference of a circle _______________
7. the area of a rectangle _______________
8. How would you find the surface area of a cylinder with no top? Give youranswer in words and symbols.
Remember What You Learned9. Complete the table.
Words The surface areaof a cylinder equals the area of
two bases plus the area of thecurved surface.
Symbols
7MG2.1
Example
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and InterventionSurface Area of Cylinders
Chapter 12 33 Glencoe California Mathematics, Grade 6
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Find the surface area of the cylinder. Use 3.14
for �. Round to the nearest tenth.
S � 2�r2 � 2�rh Surface area of a cylinder.
S � 2 � 3.14(6)2 � 2 � 3.14 (6)(20) Replace � with 3.14, r with 6, and h with 20.
� 979.7 Simplify.
The surface area is about 979.7 square meters.
Find the surface area of each cylinder. Use 3.14 for �. Round to thenearest tenth.
1. 2. 3. 4.3 cm
12 cm
3 ft
24 ft
10 in.
8 in.
20 m
6 m
The diagram below shows how you can put two circles and a rectangletogether to make a cylinder.
The surface area the area of the area of the of a cylinder equals two bases plus curved surface.
S � 2(�r 2) � (2�r)h
In the diagram above, the length of the rectangle is the same as the circumference of the circle. Also, the width of the rectangle is the same as the height of the cylinder.
20 m
6 m
Two congruentcircles...
...make up thetwo bases.
The rectanglemakes up thecurved surface.
C = 2�r C = 2�r
r
hh
Cr
� � � � �
7MG2.1
NAME ________________________________________ DATE ______________ PERIOD _____
Skills PracticeSurface Area of Cylinders
Chapter 12 34 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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-Hill, a division of T
he McG
raw-H
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panies, Inc.
12-5
Find the surface area of each cylinder. Use 3.14 for π.Round to the nearest tenth.
1. 2. 3.
4. 5. 6.
7. Find the surface area of a can with a radius of 4 centimeters and a heightof 11 centimeters.
8. Find the surface area of the outside of a cylindrical barrel with adiameter of 10 inches and a height of 12 inches.
9. Find the area of the curved surface of a D battery with a diameter of 3.2 centimeters and a height of 5.6 centimeters.
12.6 cm
6.5 cm
2 ft12
4 ft13
4.8 yd
7 yd
7 m
4 m
6 mm
10 mm
8 in.
24 in.
7MG2.1
Find the surface area of each cylinder. Use 3.14 for π.Round to the nearest tenth.
1. 2. 3.
4. 5. 6.
7. diameter � 15.2 mm 8. diameter � 28.4 yd 9. radius � 50 cmheight � 9.4 mm height � 15.1 yd height � 70 cm
ESTIMATION Estimate the area of each cylinder.
10. 11. 12.
13. FUEL STORAGE A fuel storage tank needs to be painted on the inside. Ifthe height of the tank is 40 feet and the diameter is 120 feet, what is thesurface that needs to be painted? Round to the nearest hundred squarefeet.
14. PAPER TOWELS Each of the three rolls of paper towels in a package are individually wrapped in plastic. The radius of each roll is 5.6 centimeters and the height is 27.9 centimeters. How much plastic is used to individually wrap the three rolls? Round to the nearest tenth.
2.9 yd
4.1 yd
9.9 mm
7.1 mm
6.8 ft
4.2 ft
9 ft
9 ft12
4.3 cm
8 cm
6.4 m
8.1 m
5 in.3 in.1
45.5 m
4.1 m
2 ft
7 ft
NAME ________________________________________ DATE ______________ PERIOD _____
PracticeSurface Area of Cylinders
Chapter 12 35 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
Word Problem PracticeSurface Area of Cylinders
Chapter 12 36 Glencoe California Mathematics, Grade 6
Copyright ©
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12-5
1. PACKAGING What is the area of thelabel on a box of oatmeal with a radiusof 9.3 centimeters and a height of 16.5 centimeters? Round to the nearesttenth.
2. TIRES Betty wants to know the totalsurface area of the tread on one of hertires. If the diameter of the tire is18 inches and the width of the tire is5 inches, what is the total surface areaof the tire’s tread? Round to the nearesttenth.
3. CANS A cylindrical can has a diameterof 6 inches and a height of 7.3 inches.What is the surface area of the can?Round to the nearest tenth.
4. CANS A cylindrical can has a height of14 centimeters and a radius of 4.2centimeters. Find the surface area ofthe can. Round to the nearest tenth.
5. MANUFACTURING How much sheetmetal is required to make a cylindricaltrash can with a diameter of 2 feet and
height of 4�14� feet? Round to the nearest
tenth. (Hint: Do not include the top.)
6. PLUMBING How much steel is needed tomake a hollow pipe with a radius of3 inches and a height of 15 inches?Round to the nearest tenth.
7MG2.1
NAME ________________________________________ DATE ______________ PERIOD _____
Enrichment
Chapter 12 37 Glencoe California Mathematics, Grade 6
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Cross SectionsIn each diagram on this page, a plane cuts through a solid figure. Theintersection of the plane with the solid figure is called a cross section.
Sketch the cross section formed in each diagram.
1. 2.
3. 4.
5. 6.
7. 8. (pyramid with atriangular base)
(pyramid with atriangular base)
(pyramid with asquare base)
7MG2.1
Exercises
NAME ________________________________________ DATE ______________ PERIOD _____
Scientific Calculator ActivitySurface Area of a Cylinder
Chapter 12 38 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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panies, Inc.
12-5
Find the surface area of the cylinder to the nearest tenth.
A � area of bases � area of curved surface
A � 2�r2 � 2�rh
A � 2 � � � 32 � 2 � � � 3 � 12
Enter: 2 3 2 3 12 282.7433388
To the nearest tenth, the surface area of the cylinder is 282.7 cm2.
Find the surface area of each cylinder to the nearest tenth.
1. 2.
117.8 m2 1,789.2 cm2
3. 4.
56.2 m
125 m
7.9 in.
22.4 in.
25.5 cm
8.4 cm
5 m2.5 m
ENTER
�π+x 2π
3 cm
12 cm
Pre-AP
NAME ________________________________________ DATE ______________ PERIOD _____
Student Recording SheetUse this recording sheet with pages 664–665 of the Student Edition.
Chapter 12 39 Glencoe California Mathematics, Grade 6
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Read each question. Then fill in thecorrect answer.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Record your answers for Question 12 onthe back of this paper.
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 12 40 Glencoe California Mathematics, Grade 6
12 Rubric for Scoring Pre-AP(Use to score the Pre-AP question on page 665 of the Student Edition.)
Copyright ©
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he McG
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ill Com
panies, Inc.
General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she
arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.
• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.
• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.
Exercise 12 Rubric
Score Specific Criteria4 An accurate expression that the area of the shaded region in terms of y is 36 � y2.
An accurate expression for the area of the shaded region in terms of y if thedimensions for each region were doubled is given as 144 � (2y)2 or 144 � 4y2.
3 The expressions are written correctly; however, they are written in terms of the areaof the non-shaded region instead of the area of the shaded region.
2 One of the two expressions is incorrect and the other expression is written for thearea of the entire figure.OROne of the two expressions is incorrect and the other expression is written for thearea of the non-shaded region.
1 Only one of the two expressions is correct.
0 Response is completely incorrect.
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Estimate each square root to the nearest whole number. 1.
1. �63� 2. �150� 2.
Find the missing measure of each right triangle. Round to the nearest tenth if necessary.
3. 4. 3.
4.
5. MULTIPLE CHOICE What is the side length of a right triangle if one of the sides is 28 millimeters and the hypotenuse is 35 millimeters?
A. 12 B. 21 C. 28.8 D. 40.8 5.
48 ft
14 ftc ft
9 cm12 cm
a cm
1. BOOKS In how many ways can a bookstore arrange six different books in a row for a display? 1.
2. FRAMING A portrait 14 inches by 20 inches is bordered
by a mat that is 2 inches wide. The frame around the mat
is 1�12
� inches wide. Find the area of the portrait with the
frame and mat. 2.
3. PARKS A picnic area at a park is 90 yards long and 60 yards wide. On a diagram of the park, 1 inch � 6 yards. What are the dimensions of the picnic area on the diagram? 3.
4. DRAWINGS On a scale drawing, the scale is 4 centimeters:1 meter. What is the distance in the scale drawing for a garden 8 meters by 12 meters? 4.
5. A cafeteria vending machine contains apples, chickensandwiches, potato salad, gelatin, lettuce salad, and pudding. Without looking, an employee selects one of the items. What is the probability that a salad is selected? 5.
Chapter 12 41 Glencoe California Mathematics, Grade 6
Chapter 12 Quiz 1(Lessons 12-1 and 12-2)
Chapter 12 Quiz 2(Lesson 12-3)
Ass
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
12
12
Copyright ©
Glencoe/M
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panies, Inc.
Find the surface area of each rectangular prism.
1. 2. 1.
2.
3. length � 5 cm 4. length � 22.4 mm 3.width � 5 cm width � 24.5 mmheight � 1 cm height � 20 mm 4.
5. Find the surface area of therectangular prism. 5.
6 cm
6.6 cm
11.6 cm
14 in.
16 in.62 in.
5 in.
7 in.
2.5 in.
Chapter 12 42 Glencoe California Mathematics, Grade 6
Chapter 12 Quiz 3(Lesson 12-4)
Chapter 12 Quiz 4(Lesson 12-5)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
12
12
21 cm39 cm
9 mm
8.3 mm
Find the surface area of each cylinder. Use 3.14 for π.Round to the nearest tenth.
1. 2. 1.
2.
3. 3.
4. 4.
5. Find the surface area of a cylindrical can that has a diameter of 3.6 inches and a height of 4 inches. Roundto the nearest tenth. 5.
6 m
19 m
3 in. 26 in.
Write the letter for the correct answer in the blank at the right of each question.For Questions 1-3, estimate each square root to the nearest whole number.
1. �35�A. 5 B. 6 C. 7 D. 13 1.
2. �180�F. 12 G. 13 H. 18 J. 72 2.
3. �60�A. 3,600 B. 30 C. 8 D. 7 3.
4. Use a calculator to find �87� to the nearest tenth.F. 9 G. 9.3 H. 43.5 J. 7,569.0 4.
5. Find the missing measure for the triangle.A. 625 m C. 6 mB. 25 m D. 5 m 5.
6. REMODELING How many square feet of wallpaper are needed to cover a wall that measures 14 feet by 9 feet.F. 23 ft2 H. 126 ft2
G. 63 ft2 J. 252 ft2 6.
Use a calculator to find each square root to the nearest tenth.
7. �97� 8. �106� 7.
8.
9. �224� 10. �320� 9.
10.Estimate each square root to the nearest whole number.11. �290� 12. �407� 11.
12.Find the missing measure of each right triangle. Roundto the nearest tenth if necessary. 13.
13. a � 12 cm; c � 13 cm 14. a � 11 m; c � 23 m 14.
15. SKATEBOARDING 15.A skateboarding ramp is4.5 meters long and 2.75 meters tall. To the nearesttenth, how long across the ground is the ramp?
2.75 m4.5 m
20 m
15 mc m
Chapter 12 Mid-Chapter Test(Lessons 12-1 and 12-3)
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____12
Chapter 12 43 Glencoe California Mathematics, Grade 6
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NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 12 44 Glencoe California Mathematics, Grade 6
12 Chapter 12 Vocabulary TestC
opyright ©G
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ompanies, Inc.
Choose the correct term or number to completeeach sentence.
1. The formula for finding the surface area of a (rectangular 1.prism, cylinder) is 2�w � 2�h � 2wh.
2. An irrational number is a number that cannot be written as 2.a (decimal, fraction).
3. The diagonal of a rectangle is the (leg, hypotenuse) 3.of a right triangle.
4. A leg is one of the two sides adjacent to the right 4.(angle, side) of a right triangle.
5. The (leg, hypotenuse) is the side of a right triangle 5.that is opposite the right angle.
6. To find the surface area of a (rectangular prism, cylinder), 6.you must know the radius of the base.
7. The number �5� is (rational, irrational). 7.
8. The Pythagorean Theorem describes the relationship 8.between the length of the hypotenuse and the lengths of the legs of a(n) (isosceles, right) triangle.
9. Every positive number has (one, two) square root(s). 9.
10. A rectangular prism has (6, 8) surfaces. 10.
Define each term in your own words.
11. Pythagorean Theorem
12. surface area
hypotenuse
irrational number
leg
Pythagorean Theorem
surface area
Write the letter for the correct answer in the blank at the right of each question.
1. Use a calculator to find �78� to the nearest tenth.A. 7.8 B. 8.8 C. 9.0 D. 10.8 1.
2. Estimate �37� to the nearest whole number.F. 9 G. 8 H. 7 J. 6 2.
3. Estimate �143� to the nearest whole number.A. 10 B. 11 C. 12 D. 20,499 3.
4. Estimate �899� to the nearest whole number.F. 20 G. 29 H. 30 J. 31 4.
5. Use a calculator to find �43� to the nearest tenth.A. 1,849 B. 6.6 C. 6.5 D. 3.5 5.
6. The lengths of the legs of a right triangle are 8 centimeters and6 centimeters. Which equation would you solve to find the length ofthe hypotenuse?F. 62 � x2 � 82 G. 82 � x2 � 62 H. 62 � 82 � x2 J. 82 � 62 � x2 6.
7. The length of the hypotenuse of a right triangle is 20 feet, and the lengthof one leg is 16 feet. Find the length of the other leg.A. 12 ft B. 26 ft C. 36 ft D. 72 ft 7.
8. Which could be the lengths of the sides of a right triangle?F. 30 cm, 40 cm, 50 cm H. 6 m, 8 m, 9 mG. 11 ft, 12 ft, 14 ft J. 3 cm, 4 cm, 7 cm 8.
9. ART A rectangular picture frame is 24 inches long by 18 inches wide.A diagonal brace is nailed across the back of the frame from one corner to the other. How long is the brace?A. 45 in. B. 42 in. C. 30 in. D. 21 in. 9.
10. The surface area of a cube is 150 square millimeters. What is the length of one side?F. 375 mm G. 41.7 mm H. 25 mm J. 5 mm 10.
11. Find the surface area of the rectangular prism.A. 136 mm2 C. 68 mm2
B. 80 mm2 D. 32 mm2 11.
12. CRATES Find the surface area of a crate in the shape of a rectangular
prism with a length of 5 feet, a width of 3�12� feet, and a height of 2�
12� feet.
Round to the nearest tenth.
F. 77.5 ft2 G. 44 ft2 H. 43.8 ft2 J. 22 ft2 12.
10 mm2 mm
4 mm
Chapter 12 45 Glencoe California Mathematics, Grade 6
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12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Test, Form 1C
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13. Find the surface area of the rectangular prism at the right.A. 126 cm2 C. 56 cm3
B. 90 cm2 D. 28 cm2 13.
14. Find the surface area of a cylinder with a height of 10 feet and a base with a radius of 7 feet. Round to the nearest tenth.F. 307.7 ft2 G. 747.7 ft2 H. 2,615.6 ft2 J. 2,725.5 ft2 14.
15. Find the surface area of the cylinder to the nearest tenth.A. 3,927.0 ft2 C. 471 ft2
B. 785.4 ft2 D. 157 ft2 15.
16. Find the surface area of the cylinder to the nearest tenth.F. 4,071.5 in2 H. 282.6 in2
G. 678.2 in3 J. 113.1 in2 16.
17. CANS A can of juice is 6 inches high, and its base has a radius of 2 inches. Find the surface area of the can.Round to the nearest tenth.A. 37.7 in2 B. 75.4 in2 C. 100.5 in2 D. 118.4 in2 17.
18. FRAMING A picture 12 inches by 18 inches has a frame that is 2 inches wide. Find the area of the picture with the frame.F. 216 in2 G. 252 in2 H. 280 in2 J. 432 in2 18.
19. Find the surface area of a cube with 9-centimeter edges.A. 81 cm2 B. 108 cm2 C. 324 cm2 D. 486 cm2 19.
20. Find the surface area of the cylinder. Round to the nearest tenth.
F. 1,005.3 cm2 G. 628.3 cm2 H. 408.2 cm2 J. 282.7 cm2 20.
Bonus: A cylinder has a radius of 8 centimeters and the area of its curved surface is about 351.9 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:
5 cm
8 cm
6 in
12 in
5 ft10 ft
3 cm
5 cm
6 cm
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 46 Glencoe California Mathematics, Grade 6
12 Chapter 12 Test, Form 1 (continued)C
opyright ©G
lencoe/McG
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ompanies, Inc.
Write the letter for the correct answer in the blank at the right of each question.
1. Use a calculator to find �87� to the nearest tenth.
A. 8.7 B. 9.3 C. 9.8 D. 12.4 1.
2. Estimate �90� to the nearest whole number.
F. 8 G. 9 H. 10 J. 11 2.
3. Estimate �178� to the nearest whole number.
A. 12 B. 13 C. 14 D. 19 3.
4. Estimate �1,001� to the nearest whole number.
F. 33 G. 32 H. 31 J. 20 4.
5. Use a calculator to find �267� to the nearest tenth.
A. 71,289 B. 17.4 C. 16.7 D. 16.3 5.
6. The lengths of the legs of a right triangle are 22 feet and 19 feet. Whichequation would you solve to find the length of the hypotenuse?
F. 222 � x2 � 192 H. 192 � 222 � x2
G. 192 � x2 � 222 J. 192 � 222 � x2 6.
7. The length of one leg of a right triangle is 21 inches and the length ofthe hypotenuse is 35 inches. Find the length of the other leg.
A. 12 in. B. 14 in. C. 28 in. D. 1,268.5 in. 7.
8. Which could be the lengths of the sides of a right triangle?
F. 18 m, 24 m, 30 m H. 2 cm, 3 cm, 4 cmG. 19 ft, 27 ft, 39 ft J. 56 in., 112 in., 168 in. 8.
9. TELEVISION A 41-foot guy wire is used to brace an antenna. The wire isanchored 9 feet from the base of the antenna. How tall is the antenna?
A. 80 ft B. 42 ft C. 40 ft D. 22 ft 9.
10. Find the surface area of the cylinder to the nearest tenth.
F. 508.9 cm2 H. 1,130.4 cm2
G. 876.5 cm2 J. 2,799.1 cm2 10.
11. TEA CUPS A cylindrical tea cup has a height of 70 millimeters, and its base has a radius of 30 millimeters.Find the surface area of the tea cup to the nearest tenth.
A. 2,100 mm2 C. 18,840 mm2
B. 16,014 mm2 D. 461,814.1 mm2 11.
9 cm
11 cmA
sses
smen
t
Chapter 12 47 Glencoe California Mathematics, Grade 6
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Test, Form 2AC
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12. Find the volume of the cylinder to the nearest tenth.F. 204.2 cm3 H. 314 cm3
G. 282.7 cm3 J. 1,256 cm3 12.
13. The surface area of a cube is 486 square feet. What is the length of one side?A. 9 ft C. 81 ftB. 27 ft D. 243 ft 13.
14. Find the surface area of the rectangular prism.F. 12,000 m2 H. 1,700 m2
G. 3,400 m2 J. 75 m2 14.
15. Find the surface area of a rectangular prism with a length of 60 feet, a width of 42 feet, and a height of 31 feet.A. 78,120 ft2 B. 11,364 ft2 C. 266 ft2 D. 134 ft2 15.
16. Find the surface area of the rectangular prism.F. 274 in2 H. 137 in2
G. 260 in2 J. 22 in2 16.
17. Find the surface area of a cylinder with a height of 7.1 meters and a base with a radius of 2.6 meters. Round to the nearest tenth.A. 359.7 m2 B. 158.4 m2 C. 137.2 m2 D. 18.5 m2 17.
18. CANS A cylindrical peach can has a height of 5.3 inches, and its base has a radius of 1.6 inches. Find the surface area of the peach can to the nearest tenth.F. 709.7 in2 G. 69.3 in2 H. 26.6 in2 J. 8.5 in2 18.
19. Find the surface area of the cylinder to the nearest tenth.A. 776.0 mm2 C. 4,737.5 mm2
B. 1,306.2 mm2 D. 6,371.1 mm2 19.
20. PAINTING All of a dresser’s outer surfaces need to be painted. The height of the dresser is 53 inches, its width is 21 inches, and its length is 43 inches.What is the surface area of the dresser?F. 47,859 in2 G. 8,590 in2 H. 6,784 in2 J. 4,295 in2 20.
Bonus: A cylinder has a radius of 6 centimeters and the area of its curved surface is about 150.8 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:
26 mm
3 mm
4 in. 13 in.
5 in.
15 m
20 m
40 m
10 cm
4 cm
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 48 Glencoe California Mathematics, Grade 6
12 Chapter 12 Test, Form 2A (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Write the letter for the correct answer in the blank at the right of each question.
1. Use a calculator to find �94� to the nearest tenth.A. 9.4 B. 9.7 C. 10.4 D. 12.4 1.
2. Estimate �23� to the nearest whole number.F. 4 G. 5 H. 6 J. 11 2.
3. Estimate �102� to the nearest whole number.A. 10 B. 11 C. 12 D. 25 3.
4. Estimate �520� to the nearest whole number.F. 20 G. 22 H. 23 J. 24 4.
5. Use a calculator to find �173� to the nearest tenth.A. 29,929 B. 13.2 C. 13.1 D. 5.6 5.
6. The lengths of the legs of a right triangle are 16 feet and 30 feet. Whichequation would you solve to find the length of the hypotenuse?
F. 162 � x2 � 30 H. 302 � x2 � 16G. 162 � 302 � x2 J. 302 � 162 � x2 6.
7. The length of one leg of a right triangle is 24 meters, and the length of the hypotenuse is 25 meters. Find the length of the other leg.
A. 49 m B. 35 m C. 7 m D. 1 m 7.
8. Which could be the lengths of the sides of a right triangle?
F. 7 cm, 8 cm, 10 cm H. 12 ft, 15 ft, 20 ftG. 6 cm, 8 cm, 10 cm J. 20 m, 30 m, 40 m 8.
9. TRAVEL The Garcias drove 24 miles east and then 7 miles north. Atthat point, what is the straight-line distance from their starting point?
A. 25 mi B. 31 mi C. 312.5 mi D. 625 mi 9.
10. Find the surface area of the cylinder to the nearest tenth.
F. 34,482.1 cm2 H. 4,926.0 cm2
G. 7,385.3 cm2 J. 392 cm2 10.
11. CANS A cylindrical waste can has a height of 20 inches,and its base has a radius of 10 inches. Find the surface area of the waste can to the nearest tenth.
A. 12,566.4 in2 B. 6,283.2 in2 C. 1,884 in2 D. 1,570 in2 11.
28 cm
14 cmA
sses
smen
t
Chapter 12 49 Glencoe California Mathematics, Grade 6
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Test, Form 2BC
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12. Find the surface area of the cylinder to the nearest tenth.F. 1.281.8 yd2 H. 414.5 yd2
G. 565.5 yd2 J. 301.6 yd2 12.
13. The surface area of a cube is 216 square feet. What is the length of one side?A. 72 ft B. 36 ft C. 14.7 ft D. 6 ft 13.
14. Find the surface area of the rectangular prism.F. 1,250 cm2 H. 425 cm2
G. 850 cm2 J. 80 cm2 14.
15. A rectangular prism has a length of 40 inches, a width of 22 inches,and a height of 12 inches. Find the surface area of the prism.A. 10,560 in2 B. 3,248 in2 C. 1,624 in2 D. 148 in2 15.
16. Find the surface area of the rectangular prism.F. 176 cm2 H. 5,112 cm2
G. 2,556 cm2 J. 24,480 cm2 16.
17. Find the surface area of a cylinder with a height of 19 centimeters and a base with a radius of 7 centimeters. Round to the nearest tenth.A. 307.7 cm2 B. 989.6 cm2 C. 1,143.0 cm2 D. 2,924.8 cm2 17.
18. ERASERS A cylindrical eraser has a height of 15 millimeters, and its base has a radius of 9 millimeters. Find the surface area of the eraser to the nearest tenth.F. 508.7 mm2 G. 1,102.7 mm2 H. 1,356.5 mm2 J. 3,817.0 mm2 18.
19. Find the surface area of the cylinder to the nearest tenth.A. 2,010.6 in2 C. 351.7 in2
B. 502.7 in2 D. 301.6 in2 19.
20. PAINTING All of a toy box’s outer surfaces need to be painted. The height of the toy box is 26 inches, its width is 28 inches, and its length is 38 inches. What is the surface area of the toy box?F. 2,780 in2 G. 4,104 in2 H. 5,560 in2 J. 27,664 in2 20.
Bonus: A cylinder has a radius of 9 centimeters and the area of its curved surface is about 282.7 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:
10 in.
8 in.
34 cm24 cm
30 cm
5 cm
25 cm10 cm
12 yd5 yd
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 50 Glencoe California Mathematics, Grade 6
12 Chapter 12 Test, Form 2B (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Estimate each square root to the nearest whole number. 1.
1. �29� 2. �10� 2.
3.
3. �53� 4. �78� 4.
Use a calculator to find each square root to the 5.nearest tenth. 6.
5. �90� 6. �123� 7.7. �455� 8. �69� 8.
Find the missing measure of each right triangle.Round to the nearest tenth if necessary.
9. b � 7 cm, c � 11 cm 9.
10. a � 30 ft, c � 50 ft 10.
11. 12. 11.
12.
13. A right triangle has legs that measure 22 inches and 13 inches. Find the measure of the hypotenuse. 13.
14. MUSIC In how many ways can a music store arrange five different CDs in a row for a display? 14.
15. FRAMING A picture 15 inches by 24 inches is bordered by a mat that is 2 inches wide. The frame around the
mat is 1�12
� inches wide. Find the area of the picture
with the frame and mat. 15.
16. GARDENS A garden is 14 feet long and 8 feet wide.
On a diagram of the garden, �12
� inch � 1 foot. What
are the dimensions of the garden on the diagram? 16.
4.3 m
2 m
c m
Ass
essm
ent
Chapter 12 51 Glencoe California Mathematics, Grade 6
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Test, Form 2CC
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a cm20 cm
17 cm
For Questions 17–24, find the surface area of each solid.Use 3.14 for π. Round to the nearest tenth if necessary.
17. 18. 17.
18.
19. 20. 19.
20.
21. 22. 21.
22.
23. 24. 23.
24.
25. STUNTS A monster truck attempted to scale a brick wall. 25.The highest point it reached on the wall was 3 meters. At that point, its rear wheels were 4.3 meters from the wall.How long is the monster truck? Round to the nearest hundredth.
Bonus: A cylinder has a radius of 10 centimeters and the area of its curved surface is about 502.7 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:
4 in. 8 in.
1.2 in.
7.8 in.
4 ft1.6 ft21 mm8 mm
2 cm
4.6 cm9.8 cm
11.8 ft
5 ft16 ft
2.6 m2 m
0.8 m
5 ft4 ft
11 ft
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 52 Glencoe California Mathematics, Grade 6
12 Chapter 12 Test, Form 2C (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
Estimate each square root to the nearest whole number. 1.1. �39� 2. �5� 2.
3.
3. �84� 4. �65� 4.
Use a calculator to find each square root to the 5.
nearest tenth. 6.
5. �80� 6. �109� 7.
7. �320� 8. �74� 8.
Find the missing measure of each right triangle. Roundto the nearest tenth if necessary.
9. a � 45 m, b � 60 m 9.
10. a � 5 ft, c � 8 ft 10.
11. 12. 11.
12.
13. A right triangle has legs that measure 23 centimeters and 11 centimeters. Find the measure of the hypotenuse. 13.
14. MUSIC In how many ways can a music store arrange seven different DVDs in a row for a display? 14.
15. FRAMING A picture 18 inches by 25 inches is bordered by a mat that is 2 inches wide. The frame around the mat mat is 1�
12
� inches wide. Find the area of the picture with the frame and mat. 15.
16. GARDENS A garden is 18 feet long and 9 feet wide. On a diagram of the garden, �
12
� inch � 1 foot. What are the dimensions of the garden on the diagram? 16.
c m
14 m
14.2 m6.3 cm
x cm
10 cm
Ass
essm
ent
Chapter 12 53 Glencoe California Mathematics, Grade 6
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Test, Form 2DC
opyr
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For Questions 17–24, find the surface area of each solid.Use 3.14 for π. Round to the nearest tenth if necessary.
17. 18. 17.
18.
19. 20. 19.
20.
21. 22. 21.
22.
23. 24. 23.
24.
25. STUNTS A monster truck attempted to scale a brick wall. 25.The highest point it reached on the wall was 3 meters. At that point, its rear wheels were 4.3 meters from the wall.How long is the monster truck? Round to the nearest hundredth.
Bonus: A cylinder has a radius of 11 centimeters and the area of its curved surface is about 622.0 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:
15.6 cm
14 cm
2 m
12.5 m35 yd
8 yd
8 mm 17.4 mm
30.4 mm9 ft
2 ft 5 ft
30 m24 m
31.1 m
6.5 in.6 in.
14 in.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 54 Glencoe California Mathematics, Grade 6
12 Chapter 12 Test, Form 2D (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
12 in.
6 in.
Estimate each square root to the nearest whole number. 1.1. �84� 2. �29� 2.
3.
3. �141� 4. �52� 4.
Use a calculator to find each square root to the 5.
nearest tenth. 6.
5. �68� 6. �270� 7.
7. �932� 8. �509� 8.
Find the missing measure of each right triangle.Round to the nearest tenth if necessary.
9. b � 64 m, c � 80 m 9.
10. a � 11 yd, c � 18 yd 10.
11. 12. 11.
12.
13. A right triangle has a hypotenuse that measure 42.1 centimeters and a leg that measures 36.8 centimeters.Find the measure of the other leg. 13.
14. MOVIES In how many ways can a media store arrange nine different DVDs in a row for a display? 14.
15. FRAMING A picture 15�12
� inches by 28 inches is bordered
by a mat that is 2 inches wide. The frame around the mat
is 2�12
� inches wide. Find the area of the picture with the
frame and mat. 15.
16. GARDENS A garden is 3.5 meters long and 2.8 meters wide.On a diagram of the garden, 2 centimeters � 1 meter. What are the dimensions of the garden on the diagram? 16.
8.7 in.c in.
5 in.
Ass
essm
ent
Chapter 12 55 Glencoe California Mathematics, Grade 6
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Test, Form 3C
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Inc. a cm
38.7 cm21 cm
For Questions 17–24, find the surface area of each solid.Use 3.14 for π. Round to the nearest tenth if necessary.
17. 18. 17.
18.
19. 20. 19.
20.
21. 22. 21.
22.
23. 24. 23.
24.
25. GUY WIRES A vertical pole is anchored to the ground by a 29�
34
�-foot guy wire. The wire is attached to the ground
at a point 22�12
� feet from the base of the pole. How tall is
the pole? Round to the nearest tenth. 25.
Bonus: A cylinder has a diameter of 11 centimeters and the area of its curved surface is about 414.7 square centimeters.What is the height of the cylinder? Round to the nearest whole number. B:
8 mm
60 mm
33 m
12.1 m
11 ft
8.7 ft
10 cm3.6 cm
4.8 cm
11 cm
18 cm46.1 cm
2 in.12
2 in.12
2 in.12
8 yd
4 yd
6.9 yd
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 56 Glencoe California Mathematics, Grade 6
12 Chapter 12 Test, Form 3 (continued)C
opyright ©G
lencoe/McG
raw-H
ill, a division of The M
cGraw
-Hill C
ompanies, Inc.
8.2 mm
13.5 mm
Demonstrate your knowledge by giving a clear, concise solution to each problem.Be sure to include all relevant drawings and justify your answers. You may showyour solutions in more than one way or investigate beyond the requirements ofthe problems. If necessary, record your answers on another piece of paper.
1. CARPENTRY A carpenter is framing a house.The front of the house measures 48 feet. The widthmeasures 36 feet. He measures diagonally across thehouse as shown. If the diagonal measurement is 62feet, are the corners of the house square (right angles)?Explain your reasoning. Use a calculator.
2. a. Compare the volumes and surface areas of the threeboxes pictured.
A B C
b. Compare the volumes and surface areas of the three containers pictured.A B C
c. Explain why you think manufacturers frequently package their products in tall boxes, bottles, or cans.
4 m
4 m
2 m
8 m
2 m
4 m
12 in.
6 in.2 in.
6 in.
6 in.4 in.
6 in.
6 in.2 in.
62 ft
48 ft
36 ft
Ass
essm
ent
Chapter 12 57 Glencoe California Mathematics, Grade 6
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Chapter 12 Extended-Response Test
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1. Evaluate |�8| � |�2|. (Lesson 2-1)
A 10 C 7B 6 D �10 1.
2. Write 49.5% as a decimal. (Lesson 4-7)
F 0.0495 H 84.095G 0.495 J 4.95 2.
3. Write 0.33% as a decimal. (Lesson 6-9)
A 0.0033 C 3.3B 0.033 D 33 3.
4. Find the percent of change from 18 to 41. Round to the nearestwhole percent. (Lesson 7-6)
F 44% H 128%G 56% J 228% 4.
5. RAFFLE In a raffle, one ticket will be drawn from a total of 200 tickets. If Maureen has 4 tickets, what is the probability that she will win? (Lesson 9-1)
A �510�
C 0.2
B 4% D �14� 5.
6. HORSES Tionna has a display that holds 8 horse figurines.If she has 17 horse figurines, how many combinations of 8 can she create? (Lesson 9-5)
F 40,320 H 2,312G 24,310 J 136 6.
7. Suppose �1 and �2 are complementary. If m�1 � 50º, findm�2. (Lesson 10 -1)
A 30º C 50ºB 40º D 130º 7.
8. Three sides of a triangle measure 6 meters, 4 meters, and5 meters. Classify the triangle by its sides. (Lesson 10-4)
F scalene H equilateralG isosceles J obtuse 8.
9. Triangle RST has vertices R(0, �7), S(�4, 2), and T(1, 9).Find the coordinates of S� after the figure is translated 5 units right and 7 units down. (Lesson 10 -9)
A (1, �5) B (�1, �5) C (�9, 9) D (�9, �5) 9. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 12 58 Glencoe California Mathematics, Grade 6
12 Standardized Test Practice(Chapter 1–12)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Part 1: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
10. What is the base of a parallelogram with an area of 30 squaremiles and a height of 5 miles? (Lesson 11-1)
F 152 mi H 25 miG 35 mi J 6 mi 10.
11. Find the area of a circle with a diameter of 36 millimeters.Round to the nearest tenth. (Lesson 11-4)
A 4071.5 mm2 B 113.1 mm2
B 1017.4 mm2 D 56.5 mm2 11.
12. Find the volume of a rectangular prism with a length of 5 yards,a width of 7.5 yards, and a height of 9 yards. (Lesson 11-9)
F 21.5 yd3 H 300 yd3
G 150 yd3 J 337.5 yd3 12.
13. Estimate �75� to the nearest whole number.A 8 C 38B 9 D 80 13.
14. Find the missing measure of a right triangle with side lengths of a � 5 cm and c � 9 cm.F 56 cm H 7.5 cmG 10.3 cm J 2 cm 14.
15. CABLE A 52-foot cable reaches from the top of a pole to a point on the ground that is 48 feetfrom the base of the pole. How tall is the pole?(Lesson 12-2)
A 12 ft C 50 ftB 20 ft D 92 ft 15.
16. Find the surface area of the cylinder.Round to the nearest tenth. (Lesson 12-5)
F 301.6 in2 H 424.1 in2
G 339.1 in2 J 2,120.6 in2 16.
17. Find the area of a circle with a radius of 1.5 centimeters.Round to the nearest tenth. (Lesson 11-4)
A 4.5 cm2 C 7.1 cm2
B 4.7 cm2 D 9.4 cm2 17.
18. Find the surface area in meters of a rectangular prism that is 5 meters wide, 8.5 meters long, and 2 meters high. (Lesson 12-4)
F 15.5 m2 H 85 m2
G 44.5 m2 J 139 m2 18. F G H J
A B C D
F G H J3 in. 15 in.
A B C D
52 ft
48 ft
F G H J
A B C D
F G H J
A B C D
F G H J
Chapter 12 59 Glencoe California Mathematics, Grade 6
Ass
essm
ent
12NAME ________________________________________ DATE ______________ PERIOD _____
Standardized Test Practice (continued)
(Chapter 1–12)
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19. A rectangle has a width of 3.5 inches and 19.a length of 4.25 inches. Find the perimeter of the rectangle in inches. (Lesson 3-6)
20. BAND The ratio of boys to girls in the school 20.band is 2 to 3. If there are 90 students in the band, how many of them are boys? (Lesson 6-5)
21. Use the Fundamental Counting Principle 21.to find the total number of outcomes when choosing a day in the month of September and tossing two coins. (Lesson 9-3)
22. Use the graph to tell what
22.type of translation or reflection is shown. (Lessons 10 -9, 10 -10)
23. Find the volume of the cylinder. 23.Round to the nearest tenth.(Lesson 11-10)
24. ATHLETICS A rectangular athletic field is 24.80 meters long by 60 meters wide. What is the diagonal distance across the field in meters? (Lesson 12-2)
25. WINDSTORM A strong storm blew over a billboard 27 feet tall so that it is leaning against a telephone pole 21 feet tall.(Lesson 12-2)
a. Make a drawing to represent 25a.this situation.
b. How far from the base of the telephone pole is the base of the billboard? Round to the nearest tenth if necessary. 25b.
14 in.
6 in.
y
xO
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P'
P
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Part 2: Short Response
Instructions: Write answers to short response in the space provided.
NAME ________________________________________ DATE ______________ PERIOD _____
Chapter 12 60 Glencoe California Mathematics, Grade 6
12 Standardized Test Practice (continued)
(Chapter 1–12)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
1. INTERNET For the following table, find the number of degrees for each section of a circle graph. Then make a circle graph of the data. Round to the nearest degree.
1.
For Questions 2 and 3, draw an angle having each measurement. Then classify each angle as acute,right, obtuse, or straight.
2. 60� 2.
3. 180� 3.
4. Use the graph to describe the translation from �ABC to �A�B�C�. 4.
5. Use the graph to tell what type of reflection is shown.
5.
For Questions 6 and 7, find the best name to classify 6.each quadrilateral.
6. 7. 7.
8. Find m� A in �ABC if m�B � 73° and m�C � 48°. 8.
9. PLATES Find the the circumference of a circular plate 9.that has a diameter of 14 inches. Use 3.14 for � and round to the nearest tenth if necessary.
y
xO
S'
T'
S
U'
T
U
y
xO
A' B'
AC'
C
B
Internet Use
Chapter 12 61 Glencoe California Mathematics, Grade 6
Ass
essm
ent
12NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____Unit 5 Test(Chapter 11–12)
Cop
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Internet Use
Counting Number of Households online (millions)
United States 163
Japan 135
United Kingdom 122
Canada 115
Australia 11.5
10. Estimate �75� to the nearest whole number. 10.
11. Find the missing measure of a right triangle with legs 11.8 meters and 13 meters long. Round to the nearest tenth if necessary.
For Questions 12–16, find the area of each figure. Round to the nearest tenth if necessary.
12. 13. 12.
13.
14. 15. 14.
15.
16. 16.
17. Draw a top, a side, and a front view of the following figure. 17.
18. Identify the shape of the base(s) of the figure. Then classify the figure. 18.
Find the volume and surface area of each figure.Round to the nearest tenth if necessary.
19. 20. 19.
20.
19 mm
54 mm
12 cm20 cm
19.5 cm
32 mm
40 mm
10 mm 2 cm
3 in.
6 in.
4 yd
9 yd8 yd
NAME ________________________________________ DATE ______________ PERIOD _____
SCORE _____
Chapter 12 62 Glencoe California Mathematics, Grade 6
12 Unit 5 Test (continued)
(Chapter 11–12)
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
16 ft
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ss t
han
the
squ
are
roo
t o
f 81
.
8.W
hy
are
�64�
and
�81�
use
d in
Exa
mpl
e 1?
Sam
ple
an
swer
:64
an
d81
are
per
fect
sq
uar
es,a
nd
th
ey a
re t
he
clo
sest
inte
ger
per
fect
sq
uar
es t
o 7
5.T
hey
are
use
d t
o f
ind
an
est
imat
e fo
rth
e sq
uar
e ro
ot
of
75.
Rem
emb
er W
hat
Yo
u L
earn
ed9.
Th
e ke
y to
est
imat
ing
squ
are
root
s w
ith
out
a ca
lcu
lato
r is
to
be f
amil
iar
wit
h c
omm
on p
erfe
ct s
quar
es.C
ompl
ete
the
foll
owin
g ta
ble
of c
omm
onpe
rfec
t sq
uar
es t
hen
tes
t yo
urs
elf
to s
ee h
ow m
any
you
can
rem
embe
rw
ith
out
usi
ng
a ca
lcu
lato
r.
Nu
mb
er5
67
89
1011
1213
1415
1620
25
Sq
uar
e25
3649
6481
100
121
144
169
196
225
256
400
625
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
Est
imat
ing
Sq
uar
e R
oo
ts
12-1
7NS
2.4
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Ant
icip
atio
n Gu
ide
Ext
end
ing
Alg
ebra
an
d G
eom
etry
Cha
pter
12
7G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Chapter Resources
pygp
Step
2
Step
1
ST
EP
1S
tate
men
tS
TE
P 2
A,D
,or
NS
A o
r D
1.A
squ
are
root
of
a n
um
ber
is o
ne
of i
ts t
wo
equ
al f
acto
rs.
A2.
You
can
fin
d an
est
imat
e fo
r th
e sq
uar
e ro
ot o
f 45
by
fin
din
gA
the
squ
are
root
of
the
perf
ect
squ
are
clos
est
to 4
5.3.
All
squ
are
root
s ar
e ir
rati
onal
nu
mbe
rs.
D4.
Th
e h
ypot
enu
se o
f a
righ
t tr
ian
gle
is t
he
side
opp
osit
e th
e A
righ
t an
gle.
5.S
ince
102
�62
�82
,a t
rian
gle
wh
ose
side
s h
ave
len
gth
s 6,
A8,
and
10 w
ill
be a
rig
ht
tria
ngl
e.6.
Sin
ce a
rec
tan
gula
r pr
ism
has
six
sid
es,t
he
surf
ace
area
ca
n b
e fo
un
d by
fin
din
g th
e ar
ea o
f on
e si
de a
nd
Dm
ult
iply
ing
by 6
.7.
If t
he
dim
ensi
ons
of a
rec
tan
gula
r pr
ism
are
dou
bled
,th
e D
surf
ace
area
wil
l al
so d
oubl
e.8.
If t
he
dim
ensi
ons
of a
rec
tan
gula
r pr
ism
are
dou
bled
,th
e D
volu
me
wil
l tr
iple
.9.
In f
indi
ng
the
surf
ace
area
of
a cy
lin
der,
you
are
fin
din
g th
e A
area
of
two
circ
les
and
a re
ctan
gle.
10.
Th
e u
nit
s fo
r su
rfac
e ar
ea a
re a
lway
s cu
bic
un
its
sin
ce
Dsu
rfac
e ar
ea i
nvo
lves
th
ree-
dim
ensi
onal
fig
ure
s.
Bef
ore
you
beg
in C
ha
pte
r 12
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agr
ee o
r di
sagr
ee,w
rite
NS
(N
ot S
ure
).
Aft
er y
ou c
omp
lete
Ch
ap
ter
12
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or
a D
.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D,u
se a
pie
ce o
f pa
per
to w
rite
an
ex
ampl
e of
wh
y yo
u d
isag
ree.
12
Answers (Anticipation Guide and Lesson 12-1)
Chapter 12 A1 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eE
stim
atin
g S
qu
are
Ro
ots
Cha
pter
12
11G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–1
pygp
12-1
Est
imat
e ea
ch s
qu
are
root
to
the
nea
rest
wh
ole
nu
mb
er.
1.�
5 �2
2.�
10�3
3.�
21�5
4.�
28�5
5.�
78�9
6.�
102
�10
7.�
179
�13
8.�
274
�17
9.�
303
�17
10.
�56
3�
2411
.�
592
�24
12.
�75
5�
27
13.
�98
1�
3114
.�
1,35
6�
3715
.�
1,68
8�
41
16.
�3,
287
�57
17.
�3,
985
�63
18.
�4,
125
�64
Use
a c
alcu
lato
r to
fin
d e
ach
sq
uar
e ro
ot t
o th
e n
eare
st t
enth
.
19.
�6 �
2.4
20.
�19�
4.4
21.
�30�
5.5
22.
�77�
8.8
23.
�11
4�
10.7
24.
�12
5�
11.2
25.
�14
9�
12.2
26.
�18
2�
13.5
27.
�21
2�
14.6
28.
�43
6�
20.9
29.
�62
1�
24.9
30.
�85
3�
29.2
31.
�91
8�
30.3
32.
�1,
004
�31
.733
.�
1,27
0�
35.6
34.
�5,
438
�73
.735
.�
4,21
5�
64.9
36.
�5,
786
�76
.1
37.
Ord
er �2 75 �
,4.9
1,an
d �
23�fr
om l
east
to
grea
test
.�2 75 �
,�23�
,4.9
1
38.
Gra
ph �
42�an
d �
62�on
th
e sa
me
nu
mbe
r li
ne.
01
23
45
87
64262
7NS
2.4
Exer
cise
s
Exam
ple
2
Exam
ple
1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Est
imat
ing
Sq
uar
e R
oo
ts
Cha
pter
12
10G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-1
Est
imat
e �
40�to
th
e n
eare
st w
hol
e n
um
ber
.
Lis
t so
me
perf
ect
squ
ares
.
1,4,
9,16
,25,
36,4
9,…
36�
40
�49
40 is
bet
wee
n th
e pe
rfec
t sq
uare
s 36
and
49.
�36�
��
40��
�49�
Fin
d th
e sq
uare
roo
t of
eac
h nu
mbe
r.
6�
�40�
�7
�36�
�6
and
�49�
�7
So,
�40�
is b
etw
een
6 a
nd
7.S
ince
40
is c
lose
r to
36
than
to
49,t
he
best
wh
ole
nu
mbe
res
tim
ate
is 6
.
Use
a c
alcu
lato
r to
fin
d t
he
valu
e of
�28 �
toth
e n
eare
st t
enth
.
285.
2915
0262
2
�28�
�5.
3
Ch
eck
Sin
ce 5
2�
25 a
nd
25 i
s cl
ose
to 2
8,th
e an
swer
is
reas
onab
le.
Est
imat
e ea
ch s
qu
are
root
to
the
nea
rest
wh
ole
nu
mb
er.
1.�
3�2
2.�
8�3
3.�
26�5
4.�
41�6
5.�
61�8
6.�
94�10
7.�
152
�12
8.�
850
�29
Use
a c
alcu
lato
r to
fin
d e
ach
sq
uar
e ro
ot t
o th
e n
eare
st t
enth
.
9.�
2�1.
410
.�
27�5.
2
11.
�73�
8.5
12.
�82�
9.1
13.
�10
5�
10.2
14.
�39
5�
19.9
15.
�84
6�
29.1
16.
�2,
298
�47
.9
ENTE
R2n
d
Rec
all t
hat
a pe
rfec
t sq
uare
is a
squ
are
of a
rat
iona
l num
ber.
In L
esso
n 5-
8, y
ou le
arne
d th
at a
nynu
mbe
r th
at c
an b
e w
ritte
n as
a f
ract
ion
is a
rat
iona
l num
ber.
A n
umbe
r th
at c
anno
t be
writ
ten
as a
frac
tion
is a
n ir
rati
on
al n
um
ber
.
01
23
45
6
28
7NS
2.4
Answers (Lesson 12-1)
Chapter 12 A2 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Est
imat
ing
Sq
uar
e R
oo
ts
Cha
pter
12
13G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–1
pygp
12-1
1.G
EOM
ETRY
Th
e di
amet
er d
of a
cir
cle
wit
h a
rea
Ais
giv
en b
y th
e fo
rmu
la
d�
��4 �A � �.W
hat
is
the
diam
eter
of
a
circ
le w
ith
an
are
a of
56
squ
are
inch
es?
Use
3.1
4 fo
r �
and
rou
nd
to t
he
nea
rest
ten
th.
8.4
in.
2.FE
NC
ING
Car
men
wan
ts t
o bu
y fe
nci
ng
to e
ncl
ose
a sq
uar
e ga
rden
wit
h a
nar
ea o
f 50
0 sq
uar
e fe
et.H
ow m
uch
fen
cin
g do
es C
arm
en n
eed
to b
uy?
Rou
nd
to t
he
nea
rest
ten
th.
89.4
ft
3.O
CEA
NS
Th
e sp
eed
vin
fee
t pe
r se
con
dof
an
oce
an w
ave
in s
hal
low
wat
er o
fde
pth
din
fee
t is
giv
en b
y th
e fo
rmu
lav
��
32d
�.W
hat
is
the
spee
d of
an
ocea
n w
ave
at a
dep
th o
f 10
fee
t?R
oun
d to
th
e n
eare
st t
enth
.17
.9 f
t/s
4.LI
GH
TIN
GA
new
fla
shli
ght
has
a b
eam
wh
ose
wid
th w
at a
dis
tan
ce d
from
th
efl
ash
ligh
t is
giv
en b
y th
e fo
rmu
law
�1.
2�d �.
Wh
at i
s th
e w
idth
of
the
beam
at
a di
stan
ce o
f 30
fee
t? R
oun
d to
the
nea
rest
ten
th.
6.6
ft
5.SO
UN
DT
he
spee
d of
sou
nd
in a
ir c
inm
eter
s pe
r se
con
d at
a t
empe
ratu
re T
in d
egre
es C
elsi
us
is g
iven
appr
oxim
atel
y by
th
e fo
rmu
la
c�
�40
2(T
��
273
�)�.
Wh
at i
s th
e sp
eed
of s
oun
d in
air
at
a te
mpe
ratu
re o
f 25
deg
rees
Cel
siu
s? R
oun
d to
th
en
eare
st t
enth
.34
6.1
m/s
6.PR
OJE
CTI
LES
Th
e m
uzz
le v
eloc
ity
vin
feet
per
sec
ond
nec
essa
ry f
or a
can
non
to h
it a
tar
get
xfe
et a
way
is
esti
mat
edby
th
e fo
rmu
la v
��
32x
�.W
hat
mu
zzle
velo
city
is
requ
ired
to
hit
a t
arge
t3,
000
feet
aw
ay?
Rou
nd
to t
he
nea
rest
ten
th.
309.
8 ft
/s
3,00
0 ft
7NS
2.4
Est
imat
e ea
ch s
qu
are
root
to
the
nea
rest
wh
ole
nu
mb
er.
1.�
8�3
2.�
19�4
3.�
47�7
4.�
70�8
5.�
91�10
6.�
125
�11
7.�
150
�12
8.�
389
�20
9.�
2,46
8�
5010
.�
899
�30
11.
�4,
840
�70
12.
�8,
080
�90
Use
a c
alcu
lato
r to
fin
d e
ach
sq
uar
e ro
ot t
o th
e n
eare
st t
enth
.
13.
�6�
2.4
14.
�21�
4.6
15.
�53�
7.3
16.
�79�
8.9
17.
�19
0�
13.8
18.
�62
4�
25.0
19.
�42
7�
20.7
20.
�3,
178
�56
.4
21.
�0.
36�
0.6
22.
�0.
81�
0.9
23.
�1.
44�
1.2
24.
�2.
25�
1.5
25.
ALG
EBR
AW
hat
wh
ole
nu
mbe
r is
clo
sest
to
�a
�b
�if
a�
24 a
nd
b�
38?
8
26.
ALG
EBR
AE
valu
ate
�x
�y
�to
th
e n
eare
st t
enth
if
x�
10 a
nd
y�
4.5
2.3
27.
QU
ILTI
NG
A q
uee
n-s
ize
quil
t in
th
e sh
ape
of a
squ
are
has
an
are
a of
51
squ
are
feet
.Wh
at i
s th
e ap
prox
imat
e le
ngt
h o
f on
e si
de o
f th
e qu
ilt
to t
he
nea
rest
ten
th?
7.1
ft
28.
PEN
DU
LUM
Th
e fo
rmu
la b
elow
can
be
use
d to
est
imat
e th
e ti
me
it t
akes
for
a pe
ndu
lum
to
swin
g ba
ck a
nd
fort
h o
nce
.Use
th
e fo
rmu
la t
o fi
nd
the
tim
e it
tak
es f
or a
pen
dulu
m w
ith
a l
engt
h o
f 0.
8 m
eter
to
swin
g ba
ck a
nd
fort
h o
nce
.Rou
nd
to t
he
nea
rest
ten
th.
1.8
seco
nd
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Est
imat
ing
Sq
uar
e R
oo
ts
Cha
pter
12
12G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-1
T�
2�
�L�
•T
�ti
me
(sec
onds
)•
L�
len
gth
(m
eter
s)
7NS
2.4
Answers (Lesson 12-1)
Chapter 12 A3 Glencoe California Mathematics, Grade 6
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Scie
ntifi
c Ca
lcul
ator
Act
ivity
Est
imat
ing
Sq
uar
e R
oo
ts
Cha
pter
12
15G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–1
pygp
12-1
A s
cien
tifi
c ca
lcul
ator
can
be
used
to
esti
mat
e sq
uare
roo
ts.O
n th
e T
I-34
II,
the
squa
re r
oot
func
tion
is u
sed
by p
ress
ing
the
[��]
keys
.
Est
imat
e �
1 �5 �.R
ound
to
the
near
est
hund
redt
h.
Ent
er:
[��]
15
3.87
2983
346
So,
�1 �5 �
�3.
87.
Est
imat
e �
2 �2 �.R
ound
to
the
near
est
hund
redt
h.
Ent
er:
[��]
22
4.69
0415
76
So,
�2 �2 �
�4.
69.
Est
imat
e �
1 �2 �5 �.
Rou
nd t
o th
e ne
ares
t hu
ndre
dth.
Ent
er:
[��]
125
11.18
0339
89
So,
�1 �2 �
5 ��
11.1
8.
Use
a c
alcu
lato
r to
est
imat
e ea
ch s
qu
are
root
.Rou
nd
to
the
nea
rest
hu
nd
red
th.
1.�
3 �5 �2.
�4 �2 �
3.�
3 �1 �5.
926.
485.
57
4.�
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81.
41
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9.�
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61
10.�
5 �0 �11
.�
6 �8 �12
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5 �7 �7.
078.
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55
13.�
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.�
9 �8 �15
.�
4 �4 �6.
089.
906.
63
16.�
8 �7 �17
.�
1 �5 �18
.�
1 �1 �9.
333.
873.
31
19.�
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2 �6 �3.
463.
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10
EN
TE
R
�)
2nd
EN
TE
R
�)
2nd
EN
TE
R
�)
2nd
2nd
Exam
ple
2
Exam
ple
1
Exam
ple
3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
12
14G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-1
Wo
rld
Ser
ies
Rec
ord
sE
ach
pro
ble
m g
ives
th
e n
ame
of a
fam
ous
bas
ebal
l p
laye
r.T
o fi
nd
wh
o se
t ea
ch r
ecor
d,g
rap
h t
he
poi
nts
on
th
e n
um
ber
lin
e.
1.p
itch
ed 2
3 st
rik
eou
ts i
n o
ne
Wor
ld S
erie
s
Uat
�3�,
Xat
3.3
,Kat
0.7
5,O
at �3 2�,
Fat
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2.71
bas
e h
its
in h
is a
pp
eara
nce
s in
Wor
ld S
erie
s
Bat
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at �1 16 3�
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at 0
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ns
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gle
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ld S
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s
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4.3
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at �
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nd
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ng
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age
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orld
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ies
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at �
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at 5
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at 7
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ld S
erie
s ru
ns
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aree
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at 8
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CK
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BE
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A
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32
1
48
76
5
BA
BE
RU
HT
MK
CI
YE
MA
TN
EL
812
1110
9
7NS
2.4
Answers (Lesson 12-1)
Chapter 12 A4 Glencoe California Mathematics, Grade 6
An
swer
s
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Th
e P
yth
ago
rean
Th
eore
m
Cha
pter
12
17G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–2
pygp
12-2
Fin
d t
he
mis
sin
g m
easu
re o
f a
righ
t tr
ian
gle
if a
�4
inch
es a
nd
b�
3 in
ches
.
c2�
a2�
b2P
ytha
gore
an T
heor
em
c2�
42�
32R
epla
ce a
with
4 a
nd b
with
3.
c2�
16�
9E
valu
ate
42an
d 32
.
c2�
25A
dd.
�c2 �
��
25�Ta
ke t
he p
ositi
ve s
quar
e ro
ot o
f ea
ch s
ide.
c�
5S
impl
ify.
Th
e le
ngt
h o
f th
e h
ypot
enu
se i
s 5
inch
es.
Det
erm
ine
wh
eth
er a
tri
angl
e w
ith
sid
e le
ngt
hs
of 6
met
ers,
9 m
eter
s,an
d 1
2 m
eter
s is
a r
igh
t tr
ian
gle.
c2�
a2�
b2P
ytha
gore
an T
heor
em
122
�62
�92
Rep
lace
aw
ith 6
, b
with
9,
and
cw
ith 1
2.
144
�36
�81
Sim
plify
.
144
11
7A
dd.
Th
e tr
ian
gle
is n
ota
righ
t tr
ian
gle.
Fin
d t
he
mis
sin
g m
easu
re o
f ea
ch r
igh
t tr
ian
gle.
Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.
9.8
in.
9.0
m9.
3 cm
Det
erm
ine
wh
eth
er e
ach
tri
angl
e w
ith
th
e gi
ven
sid
e le
ngt
hs
is a
righ
t tr
ian
gle.
Wri
te y
esor
no.
4.15
ft,
8 ft
,17
ftye
s5.
5 in
.,13
in
.,17
in
.n
o6.
9 yd
,40
yd,4
1 yd
yes
13 c
m
16 c
m
a cm
5 m
7.5
mcm
9 in
.
4 in
.c
in.
3 in
.
4 in
.c
in.
The
sid
es o
f a
right
tria
ngle
hav
e sp
ecia
l nam
es.T
he s
ides
adj
acen
t to
the
rig
ht a
ngle
are
the
leg
s.T
he s
ide
oppo
site
the
rig
ht a
ngle
is t
he
c2
�a2
�b
2
hyp
ote
nu
se.T
he P
yth
ago
rean
Th
eore
mde
scrib
es t
he r
elat
ions
hip
betw
een
the
leng
th o
f th
e hy
pote
nuse
and
the
leng
ths
of t
he le
gs.I
n a
right
tria
ngle
, th
e sq
uare
of
the
leng
th o
f th
e hy
pote
nuse
equ
als
the
sum
of
the
squa
res
of t
he le
ngth
s of
the
legs
.b
ac
Exam
ple
1
Exam
ple
2
7MG
3.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
T
he
Pyt
hag
ore
an T
heo
rem
Cha
pter
12
16G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-2
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n a
t th
e to
p o
f p
age
640
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.F
ind
the
area
of
each
squ
are.
9 u
nit
s2,1
6 u
nit
s2,2
5 u
nit
s2
2.H
ow a
re t
he
squ
ares
of
the
side
s re
late
d to
th
e ar
eas
of t
he
squ
ares
?T
hey
are
th
e sa
me.
3.F
ind
the
sum
of
the
area
s of
th
e tw
o sm
alle
r sq
uar
es.H
ow d
oes
the
sum
com
pare
to
the
area
of
the
larg
er s
quar
e?25
un
its2
;Th
ey a
re e
qu
al.
4.U
se g
rid
pape
r to
cu
t ou
t th
ree
squ
ares
wit
h s
ides
5,1
2,an
d 13
un
its.
For
m a
righ
t tr
ian
gle
wit
h t
hes
e sq
uar
es.C
ompa
re t
he
sum
of
the
area
s of
th
e tw
osm
alle
r sq
uar
es w
ith
th
e ar
ea o
f th
e la
rger
squ
are.
Th
ey a
re t
he
sam
e.
Rea
d t
he
Less
on
5.W
hat
doe
s th
e sy
mbo
l�
�in
dica
te?
It in
dic
ates
bo
th t
he
po
siti
vean
d n
egat
ive
squ
are
roo
t o
f a
nu
mb
er.
6.H
ow c
an y
ou f
ind
the
hyp
oten
use
of
a ri
ght
tria
ngl
e w
ith
in a
rec
tan
gle
wh
en g
iven
on
ly t
he
dim
ensi
ons
of t
he
rect
angl
e?B
y m
easu
rin
g t
he
len
gth
of
the
dia
go
nal
of
the
rect
ang
le.
7.In
Exa
mpl
es 3
an
d 4
on p
age
680,
how
do
you
kn
ow w
hic
h l
engt
h i
s c?
Sam
ple
an
swer
:c
is t
he
hyp
ote
nu
se,w
hic
h is
alw
ays
the
lon
ges
t o
f th
e th
ree
sid
es o
f a
rig
ht
tria
ng
le.
Rem
emb
er W
hat
Yo
u L
earn
ed8.
Su
mm
ariz
e w
hat
you
lea
rned
in
th
is l
esso
n b
y la
beli
ng
the
side
s of
th
eri
ght
tria
ngl
e w
ith
th
e le
tter
s a,
b,an
d c
and
then
com
plet
ing
the
tabl
e.
a
b
cY
ou c
anfi
nd
If
you
kn
owth
e le
ngt
hs
ab
,c
ba,
c
ca,
b
7MG
3.3
Answers (Lesson 12-2)
Chapter 12 A5 Glencoe California Mathematics, Grade 6
Fin
d t
he
mis
sin
g m
easu
re o
f ea
ch t
rian
gle.
Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.
13.0
cm
33.8
ft
3.9
m
4.a
�3.
3 in
.,b
�5.
6 in
.5.
b�
2.9
mm
,c�
4.4
mm
6.a
�21
yd,
c�
29 y
d
c�
6.5
in.
a�
3.3
mm
b�
20 y
d
7.a
�2�
1 5�ft
,c�
4�2 5� f
t 8.
b�
7�1 4�
in.,
c�
7�3 4�
in.
9.a
�6�
1 2�yd
,b�
10 y
d
b�
3.8
fta
�2.
7 in
.c
�11
.9 y
d
If a
tri
angl
e h
as s
ides
a,b
,an
d c
so t
hat
a2
�b2
�c2
,th
en t
he
tria
ngl
eis
a r
igh
t tr
ian
gle.
Det
erm
ine
wh
eth
er a
tri
angl
e w
ith
th
e gi
ven
sid
ele
ngt
hs
is a
rig
ht
tria
ngl
e.W
rite
yes
or n
o.
10.
9 cm
,12
cm,1
8 cm
no
11.
7 ft
,24
ft,2
5 ft
yes
12.
5 in
.,12
in
.,13
in
.ye
s
Fin
d t
he
mis
sin
g m
easu
re i
n e
ach
fig
ure
.Rou
nd
to
the
nea
rest
ten
thif
nec
essa
ry.
13.
15 m
14.
1.7
yd
15.
SOC
CER
Fin
d th
e w
idth
of
the
socc
er g
oal.
Rou
nd
to t
he
nea
rest
ten
th.
10.0
ft
16.
CO
NV
EYO
R B
ELT
Th
e di
agra
m s
how
s th
eh
oriz
onta
l di
stan
ce a
con
veyo
r be
lt m
oves
a
load
of
grav
el.I
f th
e co
nve
yor
belt
tak
es54
sec
onds
to
mov
e gr
avel
fro
m t
he
bott
omof
th
e co
nve
yor
belt
to
the
top
at a
rat
e of
3 f
eet
per
seco
nd,
how
hig
h d
oes
the
con
veyo
r be
lt l
ift
the
grav
el?
Rou
nd
to
the
nea
rest
ten
th.
61.2
ft
150
ft
h ft
5 ft
11.2
ft xft
2.5
yd
x yd
1.8
yd
30 m
x m
9 m
18 m
4.7
m
6.1
ma
m
24
ft23
.8 ft
c ft
11
cm
7 cm
c c
m
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Th
e P
yth
ago
rean
Th
eore
m
Cha
pter
12
19G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–2
pygp
12-2
7MG
3.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eT
he
Pyt
hag
ore
an T
heo
rem
Cha
pter
12
18G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-2
Fin
d t
he
mis
sin
g m
easu
re o
f ea
ch r
igh
t tr
ian
gle.
Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.18
.7 m
2.7.
1 in
.
3.8.
4 ft
4.32
.8 c
m
5.37
.9 in
.6.
1.3
yd
7.9.
5 m
8.15
.5 m
m
9.a
�15
cm
,b�
20 c
m25
cm
10.
a�
2 yd
,b�
12 y
d12
.2 y
d
11.
a�
13 i
n.,
c�
16.5
in
.10
.2 in
.12
.b
�8
mm
,c�
17 m
m15
mm
13.
a�
1.3
ft,b
�4.
6 ft
4.8
ft14
.a
�14
.7 m
,c�
23 m
17.7
m
Det
erm
ine
wh
eth
er e
ach
tri
angl
e w
ith
th
e gi
ven
sid
e le
ngt
hs
is a
righ
t tr
ian
gle.
Wri
te y
esor
no.
15.
10 f
t,24
ft,
26 f
tye
s16
.5
in.,
8 in
.,9
in.
no
17.
6 cm
,9 c
m,1
2 cm
no
18.
4.5
mm
,6.0
mm
,7.5
mm
yes
14 m
mc
mm6.
7 m
m
11.2
m
6 m
a m
2.7
yd3
yd
a yd
20.3
in.
32 in
.
c in
.
20 c
m
26 c
mx
cm12
.4 ft
a ft15
ft
5 in
.
c in
.
5 in
.7
m
b m
20 m
7MG
3.3
Answers (Lesson 12-2)
Chapter 12 A6 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
12
21G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–2
pygp
12-2
Pyth
ago
ras
in t
he
Air
In t
he
diag
ram
at
the
righ
t,an
air
plan
e h
eads
nor
th a
t 18
0 m
i/h.
Bu
t,th
e w
ind
is b
low
ing
tow
ards
th
e ea
st a
t 30
mi/h
.So,
the
airp
lan
e is
rea
lly
trav
elin
g ea
st o
f n
orth
.Th
e m
iddl
e ar
row
in
th
e di
agra
m s
how
s th
e ac
tual
dir
ecti
on o
f th
e ai
rpla
ne.
Th
e ac
tual
spe
ed o
f th
e pl
ane
can
be
fou
nd
usi
ng
the
Pyt
hag
orea
n T
heo
rem
.
�30
2�
�18
02�
��
900
��
32,4
0�
0�
��
33,3
0�
0�
�18
2.5
Th
e pl
ane’
s ac
tual
spe
ed i
s ab
out
182.
5 m
i/h.
Fin
d t
he
actu
al s
pee
d o
f ea
ch a
irp
lan
e.R
oun
d a
nsw
ers
to t
he
nea
rest
ten
th.(
You
mig
ht
wis
h t
o d
raw
a d
iagr
am t
o h
elp
you
sol
ve t
he
pro
ble
m.)
1.A
n a
irpl
ane
trav
els
at 2
40 m
i/h e
ast.
2.A
n a
irpl
ane
trav
els
at 6
20 m
i/h w
est.
A w
ind
is b
low
ing
at 2
0 m
i/h t
owar
dA
win
d is
blo
win
g at
35
mi/h
tow
ard
the
sou
th.
240.
8 m
i/hth
e so
uth
.62
1.0
mi/h
3.A
n a
irpl
ane
trav
els
at 4
50 m
i/h s
outh
.4.
An
air
plan
e tr
avel
s at
1,2
00 m
i/h e
ast.
A w
ind
is b
low
ing
at 4
0 m
i/h t
owar
dA
win
d is
blo
win
g at
30
mi/h
tow
ard
the
east
.45
1.8
mi/h
the
nor
th.
1,20
0.4
mi/h
E
N(n
ot d
raw
n to
sca
le)
180
mi/h
30 m
i/h
7MG
3.3
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Th
e P
yth
ago
rean
Th
eore
m
Cha
pter
12
20G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-2
1.O
RIG
AM
IC
hee
has
a p
iece
of
pape
rm
easu
rin
g 8.
5 in
ches
by
8.5
inch
es.I
fsh
e fo
lds
the
pape
r di
agon
ally
in
hal
f,h
ow l
ong
is t
he
fold
ed s
ide?
Rou
nd
toth
e n
eare
st t
enth
.12
.0 in
.
2.C
OM
PUTE
RS
In a
com
pute
r ca
talo
g,a
com
pute
r m
onit
or i
s sa
id t
o be
19
in
ches
.Th
is d
ista
nce
is
the
diag
onal
dist
ance
acr
oss
the
scre
en.I
f th
e sc
reen
is 1
0 in
ches
hig
h,w
hat
is
the
wid
th o
fth
e sc
reen
? R
oun
d to
th
e n
eare
st t
enth
.16
.2 in
.
3.A
NTE
NN
AS
A w
ire
10 m
eter
s lo
ng
issu
ppor
tin
g a
uti
lity
pol
e.T
he
wir
e is
anch
ored
to
the
grou
nd
and
is a
ttac
hed
to t
he
pole
9 m
eter
s ab
ove
the
grou
nd.
Wh
at i
s th
e di
stan
ce f
rom
th
e bo
ttom
of
the
pole
to
the
poin
t w
her
e th
e w
ire
isat
tach
ed t
o th
e gr
oun
d? R
oun
d to
th
en
eare
st t
enth
.4.
4 m
9 m
10 m
x m
4.R
AM
PSC
ryst
al w
ants
to
buil
d a
ram
pth
at w
ill
rise
4 f
eet
over
a h
oriz
onta
ldi
stan
ce o
f 20
fee
t.H
ow l
ong
wil
l th
era
mp
be?
Rou
nd
to t
he
nea
rest
ten
th.
20.4
ft
4 ft
20 ft
x ft
5.PO
OLS
Sal
omon
sw
ims
diag
onal
lyac
ross
his
poo
l ev
ery
day.
If S
alom
on’s
pool
is
4 m
eter
s w
ide
and
16 m
eter
sdi
agon
ally
acr
oss,
how
lon
g is
his
poo
l,to
th
e n
eare
st t
enth
of
a m
eter
?15
.5 m
6.FR
AM
ESR
osa
has
a p
ictu
re f
ram
e th
atm
easu
res
12 i
nch
es b
y 18
in
ches
.Wh
atis
th
e di
agon
al d
ista
nce
acr
oss
the
fram
e? R
oun
d to
th
e n
eare
st t
enth
.21
.6 in
.
7MG
3.3
Answers (Lesson 12-2)
Chapter 12 A7 Glencoe California Mathematics, Grade 6
Mak
e a
mod
el t
o so
lve.
1.PE
TSJa
ck’s
Pet
Sto
re h
as 5
pet
s fo
r sa
le.S
ome
are
bird
s an
d so
me
are
dogs
.Wh
en J
ack
look
s at
th
e pe
ts,h
e co
un
ts 1
8 le
gs.H
ow m
any
of e
ach
type
of
pet
are
ther
e?4
do
gs,
1 b
ird
2.IN
TER
IOR
DES
IGN
JoA
nn
is
crea
tin
g a
mod
el o
f a
livi
ng
room
.Th
e ro
om i
s
20 f
eet
by 2
0 fe
et.I
f th
e sc
ale
she
is u
sin
g is
1 f
oot
��1 2�
inch
,wh
at a
re t
he
dim
ensi
ons
of h
er m
odel
roo
m?
10 in
.by
10 in
.
3.A
RT
CO
MPE
TITI
ON
An
art
com
peti
tion
all
ows
for
subm
itte
d w
ork
to b
e n
ola
rger
th
an 1
1 in
ches
by
14 i
nch
es.I
f C
hri
sten
e’s
phot
ogra
ph i
s 8
inch
esby
10
inch
es,w
hat
is
the
larg
est
mat
te s
he
can
use
if
she
wan
ts t
he
bord
er t
o be
th
e sa
me
wid
th a
ll t
he
way
aro
un
d th
e ph
oto?
1 �1 2�
in w
ide,
so t
he
ph
oto
an
d m
atte
will
be
11 in
.by
13 in
.
tog
eth
er
4.FL
OO
RIN
GJa
mes
is
layi
ng
carp
et i
n a
n L
-sh
aped
roo
m w
hos
e m
odel
is
show
n b
elow
.How
mu
ch c
arpe
t do
es h
e n
eed?
160
ft2
5.SC
ALE
MO
DEL
Ch
arlo
tte
is b
uil
din
g a
mod
el o
f th
e E
iffe
l Tow
er.I
f th
eac
tual
tow
er i
s 98
6 fe
et t
all
and
Ch
arlo
tte’
s sc
ale
is 1
in
ch�
10 f
eet,
how
tall
is
her
mod
el?
98.6
inch
es o
r 8.
2 ft
6.SC
IEN
CE
FAIR
Au
drey
wan
ts t
o m
ake
a po
ster
th
at i
s fo
lded
in
to t
hre
ese
ctio
ns
for
her
sci
ence
fai
r pr
ojec
t.T
he
len
gth
of
the
post
er i
s 36
in
ches
.If
sh
e w
ants
th
e m
iddl
e se
ctio
n t
o be
tw
ice
the
len
gth
of
the
side
sec
tion
san
d sh
e w
ants
th
e tw
o si
de s
ecti
ons
to b
e eq
ual
,wh
at s
hou
ld b
e th
ele
ngt
h o
f th
e m
iddl
e se
ctio
n?
18 in
ches
8 ft
8 ft
8 ft
12 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
23G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–3
pygp
12-3
6MR
2.4,
6N
S2.
1Sk
ills
Prac
tice
Pro
ble
m-S
olv
ing
Inve
stig
atio
n:
Mak
e a
Mo
del
Exer
cise
s
Exam
ple
Wh
en s
olvi
ng
pro
ble
ms,
mak
e a
mod
el t
o re
pre
sen
t th
e gi
ven
sit
uat
ion
in
ord
er t
od
eter
min
e th
e b
est
pla
n f
or a
sol
uti
on.
GIF
T W
RA
PR
ita
wan
ts t
o w
rap
a r
ecta
ngu
lar
box
.Th
e b
ox i
s 12
in
ches
by
7 in
ches
by
3 in
ches
hig
h.W
hat
mu
st b
e th
e ar
ea
of t
he
pap
er s
o th
at s
he
has
a 1
in
ch o
verl
ap t
o n
eatl
y w
rap
th
e p
aper
?
1.G
AR
DEN
ING
Peg
wan
ts t
o pu
t a
ston
e pa
th 3
fee
t w
ide
arou
nd
her
rect
angu
lar
gard
en m
easu
rin
g 10
fee
t by
15
feet
.Wh
at w
ill
be t
he
peri
met
er o
f h
er g
arde
n i
ncl
udi
ng
the
ston
e pa
th?
74 f
t
2.D
RA
WIN
GD
ante
is
mak
ing
a fu
ll-s
ize
draw
ing
of h
is f
avor
ite
cart
oon
ch
arac
ter.
If t
he
figu
re i
s 1
inch
by
0.5
inch
es a
nd
his
sca
le i
s 1
inch
�10
in
ches
,how
lar
ge w
ill
the
full
siz
e ch
arac
ter
be?
10 in
.by
5 in
.
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
22G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-3
Exp
lore
You
kn
ow t
hat
th
e bo
x is
12
�7
�3
and
that
you
nee
d to
add
1 i
nch
to
som
e m
easu
res
for
the
over
lap.
You
als
o kn
ow t
hat
th
e w
rapp
ing
pape
r w
ill
be a
rec
tan
gle.
Pla
nD
raw
a s
ketc
h o
f th
e bo
x an
d th
en m
ake
a m
odel
of
the
box
if i
t w
ere
cut
apar
t an
d la
id f
lat.
You
nee
d th
e ov
erla
p go
ing
arou
nd
the
box.
Sol
veS
ketc
h t
he
box.
Mak
e a
mod
el o
f th
e bo
x u
nfo
lded
.
Th
e le
ngt
h o
f th
e pa
per
nee
ded
is t
he
dist
ance
aro
un
d th
e bo
x pl
us
1 in
ch.S
o,�
�7
�3
�7
�3
�1
or 2
1 in
ches
.T
he
wid
th o
f th
e pa
per
wou
ld b
e 3
�12
�3
or 1
8 in
ches
.T
he
area
wou
ld b
e 21
�18
or
378
in2 .
Ch
eck
Mak
e a
box
usi
ng
cen
tim
eter
s in
stea
d of
in
ches
.Th
en c
ut
a pi
ece
of p
aper
18 c
enti
met
ers
by 2
1 ce
nti
met
ers
to s
ee i
f yo
u c
an w
rap
the
box
nea
tly.
�
botto
m
front
side
side
top
back
1 in
. ove
rlap
7 in
.
12 in
.
3 in
.
12 in
.
7 in
.
3 in
.
6MR
2.4,
6N
S2.
1St
udy
Guid
e an
d In
terv
entio
nP
rob
lem
-So
lvin
g In
vest
igat
ion
:M
ake
a M
od
el
Answers (Lesson 12-3)
Chapter 12 A8 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
25G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–3
pygp
12-3
1.FO
OTB
ALL
Bil
l,D
amon
an
d S
teve
are
the
quar
terb
ack,
cen
ter
and
pun
ter
onth
e fo
otba
ll t
eam
,not
nec
essa
rily
in
that
ord
er.T
he
quar
terb
ack
and
Bil
l go
on t
he
bus
wit
h D
amon
aft
er t
he
gam
e.D
amon
is
not
th
e pu
nte
r.W
hat
pos
itio
ndo
es B
ill
play
?p
un
ter
2.SP
OR
TSJa
nel
le c
an w
alk
one
mil
e in
15
min
ute
s.H
ow l
ong
wil
l it
tak
e h
er t
ow
alk
3 m
iles
?45
min
ute
s
3.W
EATH
ERT
he
Lou
don
vill
e T
imes
pri
nts
the
foll
owin
g ch
art
show
ing
the
snow
fall
for
eac
h d
ay l
ast
wee
k.T
he
repo
rter
est
imat
es t
hat
th
ey g
ot 1
0in
ches
of
snow
du
rin
g th
e pa
st w
eek.
Isth
is a
rea
son
able
est
imat
e?ye
s
4.G
AR
DEN
ING
Th
e ta
ble
belo
w s
how
s h
owm
any
tom
atoe
s N
ich
olas
pic
ked
each
day
duri
ng
the
wee
k.H
ow m
any
does
he
nee
d to
pic
k on
Su
nda
y so
th
at h
eh
as p
icke
d a
tota
l of
20
for
the
wee
k?4
5.PA
INT
If o
ne
gall
on o
f pa
int
cove
rs 1
50sq
uar
e fe
et,i
s on
e ga
llon
en
ough
for
Su
sie
to c
over
a k
itch
en w
all
that
is
15fe
et b
y 8
feet
? Ju
stif
y yo
ur
answ
er.
yes:
15�
8�
120
squ
are
feet
6.SH
OPP
ING
Ave
ry b
ough
t a
DV
D f
or$2
2.99
an
d go
t $2
.01
back
in
ch
ange
.H
ow m
uch
did
Ave
ry g
ive
the
cash
ier?
$25.
00
7.M
ON
EYT
he
amou
nt
in C
arly
’sch
eckb
ook
is $
750
afte
r w
riti
ng
a ch
eck
for
$65
and
mak
ing
a de
posi
t of
$10
0an
d a
depo
sit
of $
75.H
ow m
uch
did
sh
est
art
wit
h i
n h
er c
hec
kboo
k?$6
40
8.V
EHIC
LES
Jim
has
15
veh
icle
s at
his
gara
ge.S
ome
are
cars
an
d so
me
are
mot
orcy
cles
.If
he
cou
nts
58
wh
eels
,h
ow m
any
of e
ach
typ
e of
veh
icle
doe
sh
e h
ave?
14 c
ars
and
1 m
oto
rcyc
le
Day
Sn
owfa
llM
onda
y1
inch
Tu
esda
y2
inch
esW
edn
esda
y0.
5 in
ches
Th
urs
day
1.5
inch
esF
rida
y3.
75 i
nch
esS
atu
rday
0 in
ches
Su
nda
y0
inch
es
Day
MT
WR
FS
S
Nu
mb
er o
f 2
53
10
5to
mat
oes
Sol
ve e
ach
pro
ble
m u
sin
g an
y st
rate
gy y
ou h
ave
lear
ned
.
6MR
2.4,
6N
S2.
1W
ord
Prob
lem
Pra
ctic
eP
rob
lem
-So
lvin
g In
vest
igat
ion
:M
ake
a M
od
elM
ixed
Pro
ble
m S
olvi
ng
Sele
ct t
he
Op
erat
ion
For
Exe
rcis
es 1
an
d 2
,mak
e a
mod
el t
oso
lve
the
pro
ble
m.
1.A
RC
HIT
ECT
Mrs
.Per
on i
s de
sign
ing
a h
ome
for
a cl
ien
t.T
he
hou
se i
s 45
fe
et b
y 76
fee
t.If
sh
e u
ses
a sc
ale
of
1 fo
ot �
�1 2�in
ch,w
hat
are
th
e di
men
sion
s of
th
e h
ouse
on
th
e bl
ue
prin
ts?
22�1 2�
in.b
y 38
in.
2.SW
IMM
ING
PO
OL
Mr.
For
rest
er h
as a
sw
imm
ing
pool
th
at m
easu
res
3�1 3�
yard
s by
8 y
ards
.If
the
deck
aro
un
d th
e po
ol
is 2
�2 3�ya
rds
wid
e,w
hat
is
the
outs
ide
peri
met
er o
f th
e de
ck?
44 y
d
Use
an
y st
rate
gy t
o so
lve
Exe
rcis
es 3
and
4.S
ome
stra
tegi
es a
re s
how
n b
elow
.
3.B
ATT
ERIE
SA
man
ufa
ctu
rin
g pl
ant
can
mak
e 35
0 ba
tter
ies
in 1
5 m
inu
tes.
How
lon
g w
ill
it t
ake
the
man
ufa
ctu
rin
gpl
ant
to m
ake
3,50
0 ba
tter
ies?
150
min
ute
s o
r 2.
5 h
ou
rs
4.SH
OPP
ING
A g
roce
ry s
tore
has
fiv
e ca
shre
gist
ers.
Abo
ut
4 cu
stom
ers
are
chec
ked
out
at e
ach
reg
iste
r ev
ery
20m
inu
tes.
How
man
y cu
stom
ers
are
chec
ked
out
at t
he
stor
e ea
ch h
our?
60 c
ust
om
ers
For
Exe
rcis
es 5
an
d 6
,sel
ect
anap
pro
pri
ate
oper
atio
n(s
) to
sol
ve t
he
pro
ble
m.J
ust
ify
you
r se
lect
ion
(s)
and
solv
e th
e p
rob
lem
.
5.TE
STS
Die
go s
core
d a
95 o
n h
is f
irst
tes
tin
sci
ence
cla
ss.H
e th
en s
core
d 10
0 on
his
nex
t 5
test
s.If
he
scor
ed a
91
on h
isse
ven
th t
est,
wh
at i
s h
is t
est
aver
age?
M
ult
iplic
atio
n,a
dd
itio
n a
nd
div
isio
n;
5�
100
�50
0;50
0�
95�
91�
686;
686
�7
�98
;te
st a
vera
ge
�98
6.N
EWSP
APE
RS
Can
dace
wan
ts t
o in
crea
seth
e n
um
ber
of n
ewsp
aper
s sh
e de
live
rs.
Sh
e cu
rren
tly
deli
vers
58
new
spap
ers.
In f
ourt
een
wee
ks,s
he
wan
ts t
o be
deli
veri
ng
100
new
spap
ers.
How
man
yn
ewsp
aper
del
iver
ies
mu
st s
he
incr
ease
each
wee
k to
obt
ain
her
goa
l?S
ub
trac
tio
n a
nd
div
isio
n;
100
�58
�42
;42
�14
�3;
3 n
ewsp
aper
s p
er w
eek
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
24G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-3 P
RO
BL
EM
-SO
LVIN
G S
TR
AT
EG
IES
•U
se t
he fo
ur-s
tep
plan
.
•D
raw
a d
iagr
am.
•U
se lo
gica
l rea
soni
ng.
•M
ake
a m
odel
.
6MR
2.4,
6N
S2.
1Pr
actic
eP
rob
lem
-So
lvin
g In
vest
igat
ion
:M
ake
a M
od
el
Answers (Lesson 12-3)
Chapter 12 A9 Glencoe California Mathematics, Grade 6
Exer
cise
s
Exam
ple
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
27G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–4
pygp
12-4
Fin
d t
he
surf
ace
area
of
the
rect
angu
lar
pri
sm.
You
can
use
th
e n
et o
f th
e re
ctan
gula
r pr
ism
to
fin
d it
s su
rfac
e ar
ea.T
her
e ar
e th
ree
pair
s of
con
gru
ent
face
s in
a
rect
angu
lar
pris
m:
�to
p an
d bo
ttom
�fr
ont
and
back
�tw
o si
des
Fac
esA
rea
top
and
bott
om(4
�3)
�(4
�3)
�24
fron
t an
d ba
ck(4
�2)
�(4
�2)
�16
two
side
s(2
�3)
�(2
�3)
�12
Su
m o
f th
e ar
eas
24 �
16 �
12 �
52
Alt
ern
ativ
ely,
repl
ace
�w
ith
4,w
wit
h 3
,an
d h
wit
h 2
in
th
e fo
rmu
la f
or s
urf
ace
area
.S
�2 �
w�
2�h
�2w
h�
2�
4�
3�
2�
4�
2�
2�
3�
2F
ollo
w o
rder
of
oper
atio
ns.
�24
�16
�12
�
52
So,
the
surf
ace
area
of
the
rect
angu
lar
pris
m i
s 52
squ
are
met
ers.
Fin
d t
he
surf
ace
area
of
each
rec
tan
gula
r p
rism
.
1.2.
3.
102
cm2
232
in2
286
ft2
5 ft
7 ft
9 ft
8 in
.
10 in
.2
in.
3 cm
3 cm
7 cm
4 m
4 m
3 m
2 m 2 m
3 m
2 m
back
side
botto
msi
de
front
top
4 m
3 m
2 m
The
sum
of
the
area
s of
all
the
surf
aces
, or
face
s, o
f a
thre
e-di
men
sion
al f
igur
e is
the
su
rfac
e ar
ea.
The
sur
face
are
a S
of a
rec
tang
ular
pris
m w
ith le
ngth
�,
wid
th w
, an
d he
ight
his
foun
d us
ing
the
follo
win
g fo
rmul
a.
S�
2�w
�2�
h�
2wh
7MG
2.1
Stud
y Gu
ide
and
Inte
rven
tion
Su
rfac
e A
rea
of
Rec
tan
gu
lar
Pri
sms
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
26G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-4
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
649
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.R
ecor
d th
e di
men
sion
s,1–
2.vo
lum
e,an
d su
rfac
e ar
ea
in a
tab
le.
2.B
uil
d tw
o m
ore
pris
ms
usi
ng
all
of t
he
cube
s.F
or e
ach
,rec
ord
the
dim
ensi
ons,
volu
me,
and
surf
ace
area
.
3.D
escr
ibe
the
pris
ms
wit
h t
he
grea
test
an
d le
ast
surf
ace
area
s.T
he
pri
sm 1
cm
�1
cm �
8 cm
has
th
e g
reat
est
surf
ace
area
.T
he
cub
e 2
cm �
2 cm
�2
cm h
as t
he
leas
t su
rfac
e ar
ea.
Rea
d t
he
Less
on
4.H
ow m
any
pair
s of
con
gru
ent
face
s ar
e th
ere
in a
rec
tan
gula
r pr
ism
?N
ame
them
.3;
top
an
d b
ott
om
,fro
nt
and
bac
k,an
d t
he
two
sid
es
5.T
ell
how
to
fin
d th
e su
rfac
e ar
ea o
f a
rect
angu
lar
pris
m i
n w
ords
.S
amp
le a
nsw
er:
Sin
ce t
he
fro
nt/
bac
k,si
de/
sid
e,an
dto
p/b
ott
om
of
a re
ctan
gu
lar
pri
sm a
re c
on
gru
ent,
you
can
fin
d t
he
area
of
on
e o
f ea
ch o
f th
e co
ng
ruen
t fa
ces
and
mu
ltip
ly it
by
two
.Th
en a
dd
th
e th
ree
area
s.
Rem
emb
er W
hat
Yo
u L
earn
ed6.
Wor
k w
ith
a p
artn
er.B
rin
g a
box
that
is
a re
ctan
gula
r pr
ism
to
clas
s (a
ny
size
,su
ch a
s a
cray
on b
ox)
that
you
can
cu
t ap
art
to f
orm
a n
et.
Lab
el t
he
surf
aces
fro
nt,
back
,top
,bot
tom
,sid
e,si
de.M
easu
re t
he
face
san
d fi
nd
the
surf
ace
area
.Use
adh
esiv
e ta
pe t
o fo
rm t
he
net
in
to a
th
ree-
dim
ensi
onal
fig
ure
.Th
en e
xch
ange
net
s w
ith
you
r pa
rtn
er.C
alcu
late
th
evo
lum
e of
th
e pr
ism
.Com
pare
th
e an
swer
s fo
un
d fr
om u
sin
g a
net
an
d a
soli
d.S
ee s
tud
ents
’wo
rk.
Dim
ensi
ons
Vol
um
eS
urf
ace
Are
a
1 cm
�1
cm �
8 cm
8 cm
334
cm
2
1 cm
�2
cm �
4 cm
8 cm
328
cm
2
2 cm
�2
cm �
2 cm
8 cm
324
cm
2
7MG
2.1
Less
on R
eadi
ng G
uide
S
urf
ace
Are
a o
f R
ecta
ng
ula
r P
rism
s
Answers (Lesson 12-4)
Chapter 12 A10 Glencoe California Mathematics, Grade 6
An
swer
s
Fin
d t
he
surf
ace
area
of
each
rec
tan
gula
r p
rism
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.
4.le
ngt
h�
20 c
m5.
len
gth
�31
.5 i
n.
6.le
ngt
h�
5.3
mm
wid
th �
18 c
mw
idth
�12
.2 i
n.
wid
th �
1.1
mm
hei
ght
�25
cm
hei
ght
�24
.8 i
n.
hei
ght
�3.
4 m
m2,
620
cm2
2,93
6.1
in2
55.2
mm
2
7.52
m2
8.11
4.6
ft2
ESTI
MA
TIO
NE
stim
ate
the
surf
ace
area
of
each
pri
sm.
9.48
6 m
m2
10.
160
in2
11.
BIR
THD
AY
GIF
TW
hen
wra
ppin
g a
birt
hda
y gi
ft f
or h
is m
oth
er,K
enji
add
san
add
itio
nal
2.5
squ
are
feet
of
gift
wra
p to
all
ow f
or o
verl
ap.H
ow m
any
squ
are
feet
of
gift
wra
p w
ill
Ken
ji u
se t
o w
rap
a gi
ft 3
.5 f
eet
lon
g,18
in
ches
wid
e,an
d 2
feet
hig
h?
33 f
t2
For
Exe
rcis
es 1
2 an
d 1
3,u
se t
he
foll
owin
g in
form
atio
n.
A c
ompa
ny
nee
ds t
o pa
ckag
e h
azar
dou
s ch
emic
als
in s
peci
al p
last
ic c
onta
iner
s th
at h
old
80 c
ubi
c fe
et o
f ch
emic
als.
12.
Fin
d th
e w
hol
e n
um
ber
dim
ensi
ons
of t
he
con
tain
er t
hat
wou
ld u
se t
he
leas
t am
oun
t of
pla
stic
.4
ft,4
ft,
and
5 f
t
13.
If t
he
plas
tic
cost
s $0
.10
per
squ
are
foot
,how
mu
ch w
ould
it
cost
to
mak
e24
con
tain
ers?
$268
.80
8.1
in.
3.8
in.
4.2
in.
8.9
mm
8.9
mm
8.9
mm
x ft7.
3 ft
3 ft
4.8
ft
5 m
3 m
2 m
x m
8
yd1 4
6
yd
12 y
d
2 3
1.6
m
5.5
m
1.2
m
2 ft
6 ft
3 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
29G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–4
pygp
12-4
468
yd2
34.6
m2
72 f
t2
7MG
2.1
Prac
tice
Su
rfac
e A
rea
of
Rec
tan
gu
lar
Pri
sms
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
28G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-4
Fin
d t
he
surf
ace
area
of
each
rec
tan
gula
r p
rism
.Rou
nd
to
the
nea
rest
ten
th i
f n
eces
sary
.
1.2.
3.
396
cm2
78 f
t260
6 in
2
4.5.
6.
522
mm
214
3 cm
212
7.8
in2
7.8.
9.
396
ft2
179.
7 in
220
5.8
mm
2
10.
A c
ube
has
a s
urf
ace
area
of
126
squ
are
feet
.Wh
at i
s th
e ar
ea o
f on
efa
ce?
21 f
t2
11.
Fin
d th
e su
rfac
e ar
ea o
f a
rect
angu
lar
pris
m t
hat
has
a l
engt
h o
f 8
inch
es,a
wid
th o
f 3
inch
es,a
nd
a h
eigh
t of
6 i
nch
es.
180
in2
6.4
mm
7.3
mm
4.1
mm
4.5
in.
4.1
in.
8.3
in.
6 ft
12 ft
7 ft
4.3
in.
6 in
.
3.7
in.
3 cm
4 cm
8.5
cm10
mm
9 m
m
9 m
m
15 in
.
9 in
.7
in.
1 ft
4 ft
7 ft
12 c
m
7 cm
6 cm
7MG
2.1
Skill
s Pr
actic
eS
urf
ace
Are
a o
f R
ecta
ng
ula
r P
rism
s
Answers (Lesson 12-4)
Chapter 12 A11 Glencoe California Mathematics, Grade 6
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
12
31G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–4
pygp
12-4
Patt
ern
Pu
zzle
s1.
Mak
e th
ree
copi
es o
f th
is
patt
ern
.Fol
d ea
ch p
atte
rn t
o m
ake
a py
ram
id.T
hen
,pu
t th
e th
ree
pyra
mid
s to
geth
er t
o m
ake
a cu
be.D
raw
a s
ketc
h o
f th
e co
mpl
eted
cu
be.
Ske
tch
es w
ill v
ary
dep
end
ing
on
th
e vi
ew c
ho
sen
.
2.M
ake
fou
r co
pies
of
this
pat
tern
.F
old
each
pat
tern
to
mak
e a
soli
d fi
gure
.Th
en,p
ut
the
fou
r so
lids
to
geth
er t
o m
ake
a py
ram
id.M
ake
a sk
etch
of
the
fin
ish
ed p
yram
id.
Ske
tch
es w
ill v
ary
dep
end
ing
on
th
e vi
ew c
ho
sen
.
3.F
ind
the
surf
ace
area
of
the
cube
in
Exe
rcis
e 1.
54 c
m2
7MG
2.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Cha
pter
12
30G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-4
1.PA
CK
AG
ING
A p
acka
gin
g co
mpa
ny
nee
ds t
o kn
ow h
ow m
uch
car
dboa
rdw
ill
be r
equ
ired
to
mak
e bo
xes
18 i
nch
es l
ong,
12 i
nch
es w
ide,
and
10 i
nch
es h
igh
.H
ow m
uch
car
dboa
rdw
ill
be n
eede
d fo
r ea
ch b
ox i
f th
ere
isn
o ov
erla
p in
th
e co
nst
ruct
ion
?
1,03
2 in
2
2.IN
SULA
TIO
NJa
ne
nee
ds t
o bu
yin
sula
tion
for
th
e in
side
of
a tr
uck
con
tain
er.
Th
e co
nta
iner
is
are
ctan
gula
r pr
ism
15
feet
lon
g,8
feet
wid
e,an
d 7 �
1 2�fe
et h
igh
.How
mu
ch
insu
lati
on s
hou
ld J
ane
buy
if a
ll i
nsi
desu
rfac
es e
xcep
t th
e fl
oor
are
to b
ein
sula
ted?
465
ft2
3.IC
ES
upp
ose
the
len
gth
of
each
edg
e of
a cu
be o
f ic
e is
4 c
enti
met
ers.
Fin
d th
esu
rfac
e ar
ea o
f th
e cu
be.
96 c
m2
4 cm
4.IC
ES
upp
ose
you
cu
t th
e ic
e cu
be f
rom
Exe
rcis
e 3
in h
alf
hor
izon
tall
y in
to t
wo
smal
ler
rect
angu
lar
pris
ms.
Fin
d th
esu
rfac
e ar
ea o
f on
e of
th
e tw
o sm
alle
rpr
ism
s.64
cm
2
5.C
ON
TAIN
ERS
Wh
at i
s th
e to
tal
surf
ace
area
of
the
insi
de a
nd
outs
ide
of a
con
tain
er i
n t
he
shap
e of
a r
ecta
ngu
lar
pris
m w
ith
len
gth
of
5 m
eter
s,w
idth
of
3 m
eter
s,an
d h
eigh
t of
2.2
met
ers?
130.
4 m
2
6.TO
YS
Osc
ar i
s m
akin
g a
play
blo
ck f
orh
is b
aby
sist
er b
y gl
uin
g fa
bric
ove
r th
een
tire
su
rfac
e of
a f
oam
blo
ck.H
owm
uch
fab
ric
wil
l O
scar
nee
d?
66.7
in2
6.1
in.
2.3
in.
2.3
in.
7MG
2.1
Wor
d Pr
oble
m P
ract
ice
Su
rfac
e A
rea
of
Rec
tan
gu
lar
Pri
sms
Answers (Lesson 12-4)
Chapter 12 A12 Glencoe California Mathematics, Grade 6
An
swer
s
Exam
ple
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Stud
y Gu
ide
and
Inte
rven
tion
Su
rfac
e A
rea
of
Cyl
ind
ers
Cha
pter
12
33G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–5
pygp
12-5
Fin
d t
he
surf
ace
area
of
the
cyli
nd
er.U
se 3
.14
for
�.R
oun
d t
o th
e n
eare
st t
enth
.
S�
2�r2
�2�
rhS
urfa
ce a
rea
of a
cyl
inde
r.
S�
2 �
3.14
(6)2
�2
�3.
14(6
)(20
)R
epla
ce �
with
3.1
4, r
with
6,
and
hw
ith 2
0.
�97
9.7
Sim
plify
.
Th
e su
rfac
e ar
ea i
s ab
out
979.
7 sq
uar
e m
eter
s.
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er.U
se 3
.14
for
�.R
oun
d t
o th
en
eare
st t
enth
.
1.2.
3.
408.
2 in
250
8.7
ft2
440.
2 cm
2
4.3
cm
12 c
m
3 ft 24
ft
10 in
. 8 in
.
20 m
6 m
The
dia
gram
bel
ow s
how
s ho
w y
ou c
an p
ut t
wo
circ
les
and
a re
ctan
gle
toge
ther
to
mak
e a
cylin
der.
The
sur
face
are
ath
e ar
ea o
fth
e ar
ea o
f th
e of
a c
ylin
der
equa
lstw
o ba
ses
plus
curv
ed s
urfa
ce.
S�
2(�
r2)
�(2
�r)
h
In t
he d
iagr
am a
bove
, th
e le
ngth
of
the
rect
angl
e is
the
sam
e as
the
ci
rcum
fere
nce
of t
he c
ircle
.Als
o, t
he w
idth
of
the
rect
angl
e is
the
sam
e as
the
hei
ght
of t
he c
ylin
der.
20 m
6 m
Two
cong
ruen
tci
rcle
s...
...m
ake
up th
etw
o ba
ses.
The
rect
angl
em
akes
up
the
curv
ed s
urfa
ce.
C =
2�r
C =
2�r
r
hh C
r
�����
7MG2.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Less
on R
eadi
ng G
uide
S
urf
ace
Are
a o
f C
ylin
der
s
Cha
pter
12
32G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-5
Get
Rea
dy
for
the
Less
on
Com
ple
te t
he
Min
i L
ab a
t th
e to
p o
f p
age
656
in y
our
text
boo
k.W
rite
you
r an
swer
s b
elow
.
1.M
ake
a n
et o
f th
e cy
lin
der.
Sam
ple
an
swer
:
2.N
ame
the
shap
es i
n t
he
net
.ci
rcle
,rec
tan
gle
3.H
ow i
s th
e le
ngt
h o
f th
e re
ctan
gle
rela
ted
to t
he
circ
les?
Th
e le
ng
tho
f th
e re
ctan
gle
is t
he
circ
um
fere
nce
of
the
circ
le.S
o,t
he
len
gth
is 2
�r.
4.E
xpla
in h
ow t
o fi
nd
the
surf
ace
area
of
the
cyli
nde
r.A
dd
th
e ar
eas
of
bo
th c
ircl
es a
nd
th
e ar
ea o
f th
e re
ctan
gle
.
Rea
d t
he
Less
on
Wri
te t
he
form
ula
to
use
to
fin
d e
ach
of
the
foll
owin
g.
5.th
e ar
ea o
f a
circ
le
____
____
____
___
A�
�r2
6.th
e ci
rcu
mfe
ren
ce o
f a
circ
le
____
____
____
___
C�
2�r
7.th
e ar
ea o
f a
rect
angl
e _
____
____
____
__A
�b
h
8.H
ow w
ould
you
fin
d th
e su
rfac
e ar
ea o
f a
cyli
nde
r w
ith
no
top?
Giv
e yo
ur
answ
er i
n w
ords
an
d sy
mbo
ls.
Sam
ple
an
swer
:F
ind
th
e ar
ea o
fth
e b
ase
and
ad
d it
to
th
e ar
ea o
f th
e cu
rved
su
rfac
e;S
��
r2�
2�rh
.
Rem
emb
er W
hat
Yo
u L
earn
ed9.
Com
plet
e th
e ta
ble.
Wor
ds
Th
e su
rfac
e ar
eaof
a c
ylin
der
equ
als
the
area
of
two
base
spl
us
the
area
of
the
curv
ed s
urf
ace.
Sym
bol
sS
�2(
�r2
)�
(2�
r)h
7MG
2.1
Answers (Lesson 12-5)
Chapter 12 A13 Glencoe California Mathematics, Grade 6
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er.U
se 3
.14
for π.
Rou
nd
to
the
nea
rest
ten
th.
1.50
.2 f
t22.
3.
4.5.
6.
7.di
amet
er�
15.2
mm
8.di
amet
er �
28.4
yd
9.ra
diu
s �
50 c
mh
eigh
t �
9.4
mm
hei
ght
�15
.1 y
dh
eigh
t �
70 c
m81
1.4
mm
22,
612.
9 yd
237
,680
cm
2
ESTI
MA
TIO
NE
stim
ate
the
area
of
each
cyl
ind
er.
10.
11.
12.
Sam
ple
an
swer
:S
amp
le a
nsw
er:
Sam
ple
an
swer
:2
�3
� 22
�2
�3
�2
�7
2�
3�
102
�2
�3
�10
�7
2�
3�
32�
2�
3�
3�
4 o
r 10
8 ft
2o
r 1,
020
mm
2o
r 12
6 yd
2
13.
FUEL
STO
RA
GE
A f
uel
sto
rage
tan
k n
eeds
to
be p
ain
ted
on t
he
insi
de.I
fth
e h
eigh
t of
th
e ta
nk
is 4
0 fe
et a
nd
the
diam
eter
is
120
feet
,wh
at i
s th
esu
rfac
e th
at n
eeds
to
be p
ain
ted?
Rou
nd
to t
he
nea
rest
hu
ndr
ed s
quar
efe
et.
37,6
80 f
t2
14.
PAPE
R T
OW
ELS
Eac
h o
f th
e th
ree
roll
s of
pap
er t
owel
s in
a p
acka
ge a
re
indi
vidu
ally
wra
pped
in
pla
stic
.Th
e ra
diu
s of
eac
h r
oll
is 5
.6 c
enti
met
ers
and
the
hei
ght
is 2
7.9
cen
tim
eter
s.H
ow m
uch
pla
stic
is
use
d to
in
divi
dual
ly w
rap
the
thre
e ro
lls?
Rou
nd
to t
he
nea
rest
ten
th.
3,53
4.4
cm2
2.9
yd
4.1
yd
9.9
mm 7.
1 m
m
6.8
ft
4.2
ft
9 ft
9
ft1 2
4.3
cm 8 cm
6.4
m 8.1
m
5 in
.3
in
.1 4
5.5
m
4.1
m
2 ft 7 ft
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Prac
tice
Su
rfac
e A
rea
of
Cyl
ind
ers
Cha
pter
12
35G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–5
pygp
12-5
331.
6 m
290
.3 in
2
227.
1 m
233
2.1
cm2
395.
6 ft
2
7MG
2.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Skill
s Pr
actic
eS
urf
ace
Are
a o
f C
ylin
der
s
Cha
pter
12
34G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-5
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er.U
se 3
.14
for π.
Rou
nd
to
the
nea
rest
ten
th.
1.2.
3.
1,60
7.7
in2
602.
9 m
m2
276.
3 m
2
4.5.
6.
355.
7 yd
210
7.3
ft2
506.
4 cm
2
7.F
ind
the
surf
ace
area
of
a ca
n w
ith
a r
adiu
s of
4 c
enti
met
ers
and
a h
eigh
tof
11
cen
tim
eter
s.37
6.8
cm2
8.F
ind
the
surf
ace
area
of
the
outs
ide
of a
cyl
indr
ical
bar
rel
wit
h a
diam
eter
of
10 i
nch
es a
nd
a h
eigh
t of
12
inch
es.
533.
8 in
2
9.F
ind
the
area
of
the
curv
ed s
urf
ace
of a
D b
atte
ry w
ith
a d
iam
eter
of
3.2
cen
tim
eter
s an
d a
hei
ght
of 5
.6 c
enti
met
ers.
56.3
cm
2
12.6
cm 6.
5 cm
2
ft1 2
4
ft1 3
4.8
yd
7 yd
7 m
4 m
6 m
m
10 m
m
8 in
. 24 in
.
7MG
2.1
Answers (Lesson 12-5)
Chapter 12 A14 Glencoe California Mathematics, Grade 6
An
swer
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Enri
chm
ent
Cha
pter
12
37G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Lesson 12–5
pygp
12-5
Cro
ss S
ecti
on
sIn
eac
h d
iagr
am o
n t
his
pag
e,a
plan
e cu
ts t
hro
ugh
a s
olid
fig
ure
.Th
ein
ters
ecti
on o
f th
e pl
ane
wit
h t
he
soli
d fi
gure
is
call
ed a
cro
ss s
ecti
on.
Sk
etch
th
e cr
oss
sect
ion
for
med
in
eac
h d
iagr
am.
1.2.
3.4.
5.6.
7.8.
(pyr
am
id w
ith
atr
ian
gu
lar
ba
se)
(pyr
am
id w
ith
atr
ian
gu
lar
ba
se)
(pyr
am
id w
ith
asq
ua
re b
ase
)
7MG
2.1
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Wor
d Pr
oble
m P
ract
ice
Su
rfac
e A
rea
of
Cyl
ind
ers
Cha
pter
12
36G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-5
1.PA
CK
AG
ING
Wh
at i
s th
e ar
ea o
f th
ela
bel
on a
box
of
oatm
eal
wit
h a
rad
ius
of 9
.3 c
enti
met
ers
and
a h
eigh
t of
16
.5 c
enti
met
ers?
Rou
nd
to t
he
nea
rest
ten
th.
963.
7 cm
2
2.TI
RES
Bet
ty w
ants
to
know
th
e to
tal
surf
ace
area
of
the
trea
d on
on
e of
her
tire
s.If
th
e di
amet
er o
f th
e ti
re i
s18
in
ches
an
d th
e w
idth
of
the
tire
is
5 in
ches
,wh
at i
s th
e to
tal
surf
ace
area
of t
he
tire
’s t
read
? R
oun
d to
th
e n
eare
stte
nth
.28
2.6
in2
3.C
AN
SA
cyl
indr
ical
can
has
a d
iam
eter
of 6
in
ches
an
d a
hei
ght
of 7
.3 i
nch
es.
Wh
at i
s th
e su
rfac
e ar
ea o
f th
e ca
n?
Rou
nd
to t
he
nea
rest
ten
th.
194.
1 in
2
4.C
AN
SA
cyl
indr
ical
can
has
a h
eigh
t of
14 c
enti
met
ers
and
a ra
diu
s of
4.2
cen
tim
eter
s.F
ind
the
surf
ace
area
of
the
can
.Rou
nd
to t
he
nea
rest
ten
th.
480.
0 cm
2
5.M
AN
UFA
CTU
RIN
GH
ow m
uch
sh
eet
met
al i
s re
quir
ed t
o m
ake
a cy
lin
dric
altr
ash
can
wit
h a
dia
met
er o
f 2
feet
an
d
hei
ght
of 4
�1 4�fe
et?
Rou
nd
to t
he
nea
rest
ten
th.
(Hin
t:D
o n
ot i
ncl
ude
th
e to
p.)
29.8
ft2
6.PL
UM
BIN
GH
ow m
uch
ste
el i
s n
eede
d to
mak
e a
hol
low
pip
e w
ith
a r
adiu
s of
3 in
ches
an
d a
hei
ght
of 1
5 in
ches
?R
oun
d to
th
e n
eare
st t
enth
.28
2.6
in2
7MG
2.1
Answers (Lesson 12-5)
Chapter 12 A15 Glencoe California Mathematics, Grade 6
Exer
cise
s
NA
ME
____
____
____
____
____
____
____
____
____
____
DAT
E _
____
____
____
_P
ER
IOD
__
___
Scie
ntifi
c Ca
lcul
ator
Act
ivity
Su
rfac
e A
rea
of
a C
ylin
der
Cha
pter
12
38G
lenc
oe C
alifo
rnia
Mat
hem
atic
s, G
rade
6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12-5
Fin
d th
e su
rfac
e ar
ea o
f th
e cy
linde
r to
the
nea
rest
ten
th.
A�
area
of
base
s �
area
of
curv
ed s
urfa
ce
A�
2�r2
�2�
rh
A�
2�
��
32�
2�
��
3�
12
Ent
er:
2 3
2 3
12
282.
7433
388
To t
he n
eare
st t
enth
, the
sur
face
are
a of
the
cyl
inde
r is
282
.7 c
m2 .
Fin
d t
he
surf
ace
area
of
each
cyl
ind
er t
o th
e n
eare
st t
enth
.
1.11
7.8
m2
2.1,
789.
2 cm
2
117.
8 m
21,
789.
2 cm
2
3.1,
504.
0 in
24.
63,9
84.4
m2
56.2
m
125
m
7.9
in.
22.4
in.
25.5
cm
8.4
cm
5 m
2.5
m
EN
TE
R
�
π
+
x2
π
3 cm
12 c
m
Answers (Lesson 12-5)
Chapter 12 A16 Glencoe California Mathematics, Grade 6
Chapter 12 A17 Glencoe California Mathematics, Grade 6
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.Chapter 12 Assessment Answer Key
Quiz 1 (Lessons 12-1 and 12-2) Quiz 3 (Lesson 12-4) Mid-Chapter TestPage 41 Page 42 Page 43
Quiz 2 (Lesson 12-3)
Page 41
Quiz 4 (Lesson 12-5)
Page 42
1.
2.
3.
4.
5. B
7.9 cm
50 ft
12
8
1.
2.
3.
4.
5.�13
�
32 cm by 48 cm
15in. by 10 in.
567 in2
720
1.
2.
3.
4.
5. 130 in2
2,973.6 mm2
70 cm2
371.52 cm2
4,168 in2
1.
2.
3.
4.
5. 65.6 in2
361.7 mm2
7,912.8 cm2
942 m2
546.4 in2
1.
2.
3.
4.
5.
6. H
B
G
C
G
B
7.
8.
9.
10.
11.
12.
13.
14.
15. 3.6 m
20.2 m5 cm
20
17
17.9
15.0
10.3
9.8
An
swer
s
Chapter 12 Assessment Answer KeyVocabulary Test Form 1Page 44 Page 45 Page 46
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Sample answer: the sum of the areas of all the surfaces of a solid
Sample answer: a theorem that says that in a right triangle,the square of the length of thehypotenuse equals the sum of the squares of the lengths of the legs
6
two
right
irrational
cylinder
hypotenuse
angle
hypotenuse
fraction
rectangular prism
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12. F
A
J
C
F
A
H
B
H
C
J
B 13.
14.
15.
16.
17.
18.
19.
20. H
D
H
C
H
C
G
A
B: 7 cm
Chapter 12 A18 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Chapter 12 A19 Glencoe California Mathematics, Grade 6
An
swer
s
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.Chapter 12 Assessment Answer Key
Form 2A Form 2BPage 47 Page 48 Page 49 Page 50
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. B
H
C
F
C
H
D
G
B
G
B 12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 4 cm
G
B
G
B
F
B
G
A
H 1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. D
G
A
G
C
G
B
H
A
G
B 12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 5 cm
H
C
H
C
H
B
G
D
H
Chapter 12 A20 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.Chapter 12 Assessment Answer Key
Form 2CPage 51 Page 52
1.
2.
3.
4.
5.
6.
7.8.
9.
10.
11.
12.
13.
14.
15.
16. 7 in. by 4 in.
682 in2
120
25.6 in.
10.5 cm
4.7 m
40 ft
8.5 cm
8.321.311.1
9.5
973
5 17.
18.
19.
20.
21.
22.
23.
24.
25.
B: 8 cm
5.24 m
301.4 in2
440.9 in2
56.3 ft2
628 mm2
147.8 cm2
655.6 ft2
17.8 m2
238 ft2
Chapter 12 A21 Glencoe California Mathematics, Grade 6
An
swer
s
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c.Chapter 12 Assessment Answer Key
Form 2DPage 53 Page 54
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16. 9 in. by 4.5 in.
800 in2
5,040
25.5 m
19.9 m
7.8 cm
6.2 ft
75 m
8.6
17.910.48.9
8926 17.
18.
19.
20.
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22.
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24.
25.
B: 9 cm
5.24 m
678.2 in2
2,899.9 cm2
182.1 m2
979.7 yd2
1,822.7 mm2
146 ft2
4,798.8 m2
428 in2
Chapter 12 A22 Glencoe California Mathematics, Grade 6
Copyright ©
Glencoe/M
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he McG
raw-H
ill Com
panies, Inc.Chapter 12 Assessment Answer Key
Form 3Page 55 Page 56
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16. 7 cm by 5.6 cm
906.5 in2
362,880
20.4 cm
32.5 cm
10.0 in.
14.2 yd
48 m
22.6
30.516.48.2
71259 17.
18.
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B: 12 cm
19.5 ft
633.7 mm2
3,416.3 mm2
3,427.1 m2
419.3 ft2
202.6 cm2
3,069.8 cm2
37.5 in2
229.6 yd2
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c.
Chapter 12 A23 Glencoe California Mathematics, Grade 6
An
swer
s
Chapter 12 Assessment Answer Key Page 57, Extended-Response Test
Scoring Rubric
Level Specific Criteria
4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.
3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.
2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.
1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.
0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.
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Chapter 12 A24 Glencoe California Mathematics, Grade 6
Chapter 12 Assessment Answer Key Page 57, Extended-Response Test
Sample Answers
1. No; �482 �� 362� equals 60, not 62.2. a. Volume of A: 72 in3
Volume of B: 144 in3
Volume of C: 144 in3
2 � Volume A � Volume B �Volume CSurface Area of A: 120 in2
Surface Area of B: 168 in2
Surface Area of C: 216 in2
Surface Area of A � 48 � SurfaceArea of BSurface Area of B � 48 � SurfaceArea of C
b. Volume of A: 50.3 m3
Volume of B: 100.5 m3
Volume of C: 201.1 m3
4 � Volume A � 2 � Volume B �Volume CSurface Area of A: 75.4 m2
Surface Area of B: 125.7 m2
Surface Area of C: 201.1 m2
Surface Area of C � Surface Area ofB � Surface Area of A
c. An increase in height gives theappearance of a larger increase insurface area and volume than doesan increase in width, depth, orradius.
In addition to the scoring rubric found on page A23, the following sample answersmay be used as guidance in evaluating extended-response assessment items.
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Chapter 12 A25 Glencoe California Mathematics, Grade 6
An
swer
s
Chapter 12 Assessment Answer KeyStandardized Test PracticePage 58 Page 59
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9. A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D 10.
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18. F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
A B C D
F G H J
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Chapter 12 A26 Glencoe California Mathematics, Grade 6
1
Chapter 12 Assessment Answer KeyStandardized Test PracticePage 60
19.
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25a.
25b. 17.0 ft
pole21 ft
board27 ft
x ft
100 m
923.2 in3
Reflection overthe x-axis
120 outcomes
36
15.5
Chapter 12 A27 Glencoe California Mathematics, Grade 6
Ass
essm
ent
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c.Chapter 12 Assessment Answer Key
Unit 5 Test Page 61 Page 62
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9. 44.0 in.
59°
rhombus
quadrilateral
reflection over y-axis
7 units right and 5 units up
straight
180˚acute
60˚
U.S., 245�; Japan, 53�;U.K, 33�; Canada, 23�;
Australia, 8�
Internet Use
UnitedStates68%
UK9%
Australia2%
Japan15%
Canada6%
10.
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17.
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20.61,211.2 mm3;8,710.4 mm2
4,680 cm3; 1,728 cm2
rectangle; rectangularpyramid
top side front
71.5 ft2
360 mm2
12.6 cm2
9 in2
32 yd2
15.3 m
9
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