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Name: ___________________________
Geometry Period _______
Unit 11: Solid Geometry
In this unit you must bring the following materials with you to class every day:
Calculator Pencil
This Booklet
A device
Headphones!
Please note:
You may have random material checks in class
Some days you will have additional handouts to support your understanding of
the learning goals in that lesson. Keep these in a folder and bring to class every
day.
All homework for part one of this unit is in this booklet.
Answer keys will be posted as usual for each daily lesson on our website
3D Figures Formed by Translations
Learning goal: How are 3D figures formed through translations and what are the properties of these solids?
Imagine this! You stand inside a hula hoop, which is dipped in bubble solution.
Lift the hula hoop straight up.
>>Can you sketch the shape that the bubble will take?
>>Do you know what this is called?
>> What objects do you know that take this shape?
Google Sketch Up! Thinking in 3-D... Circles Sketch the 2D preimage Sketch the 3D figure formed when a circle is translated
into 3 dimensions.
Conclusion: when a circle is translated into 3D, and we trace it’s path, a ____________ is formed.
New Vocab Alert!
>>Base View (base): >>Lateral View (lateral face):
Making Connections:
The base view of a cylinder is a ___________________. The lateral view of a cylinder is a _____________________.
All about Cylinders!
A cylinder is... A 3-D figure.
Two circular bases that are ____________ and ______________.
Lateral faces are ______________.
Can be formed when a circle is translated (“Pushed”) into 3-D.
Other Important Properties: Like a prism, but the bases are NOT polygons.
11-1 Notes
Further Thinking: What happens when the shape we start with is not a circle? What
if the preimage is a polygon?
Let’s see this in “Sketch-Up!”
What shape are we are starting with?
o This preimage would be the ____________.
The resulting figure is a ______________________.
Sketch the 2D preimage Sketch the 3D figure formed when a circle is translated
into 3 dimensions.
Conclusion: when a triangle is translated into 3D, and we trace it’s path, a ____________ is formed.
Making Connections:
The base view of a triangular prism is a ____________________. The lateral view of a triangular prism is a _________________.
What type of transformation would map the blue triangle onto the red triangle?
If we trace the path of the pre-image, what 3D figure is formed?
All about Prisms A prism is...
A 3D figure. Formed by translating any polygon. Two polygonal bases that are ____________ and _____________.
Other Important Properties
Prisms are named by their _________________.
Lateral faces are always ___________________. o Special case: Cubes all their faces are ___________.
Lateral Edges (the lines formed when the faces meet) are always ___________ and ____________.
The number of lateral faces corresponds to the number of ___________ the base has.
Another example:
What shape are we are starting with? ______________
o This preimage would be the ____________.
The resulting figure is a ______________________.
Sketch the 2D preimage Sketch the 3D figure formed when a circle is translated into 3 dimensions.
Conclusion: when a pentagon is translated into 3D, and we trace it’s path, a ____________ is formed.
Making Connections:
The base view of a pentagonal prism is a ___________________. The lateral view of a pentagonal prism is a _________________.
Cross Sections The 2D shape that appears when you cut/slice a 3D solid with a plane. Two Special Types! Cross sections parallel to the base are the same as the
____________ view.
Cross sections perpendicular to the base are the same as the ___________ view.
Shape Cross Section parallel to the base
(same shape as base view)
Cross Section perpendicular to the base
(same shape as lateral view)
Cyldiner
Shape: ___________
Shape: __________
Pentagonal Prism
Shape: ___________
Shape: ___________
Trianglular Prsim
Shape: ___________
Shape: ___________
As a class! When we translated a rectangle into 3-D, the result was a _______________.
What transformation(s) do you think are required to create the 3d figure to the right, if the "pre-image" is still a square?
All about Pyramids
A pyramid is... A 3D solid Formed by a ____________and a ___________.
Other Important Properties:
One base that is a polygon. Named by the base polygon. Lateral edges are congruent. Lateral faces are Isosceles triangles.
Practice
Applying our Knowledge 1. Name each of the solids below. Draw the base and lateral views and name the cross sections.
Name: ___________
Name: ___________
Name: __________
Base View (name and sketch):
What 2D shape is the cross section
parallel to the base?
Base View (name and sketch):
What 2D shape is the cross section
parallel to the base?
Base View (name and sketch):
What 2D shape is the cross section
parallel to the base?
Lateral View (name and sketch):
What 2D shape is the cross section
that is perpendicular to the base?
Lateral View (name and sketch):
What 2D shape is the cross section
that is perpendicular to the base?
Lateral View (name and sketch):
What 2D shape is the cross section
that is perpendicular to the base?
2. A square piece of fabric is laid out on the ground and the corners are hammered in place. A pole is placed under the fabric at its center and used to raise a shelter.
a) What 3d figure is formed? b) What is the base view? c) What is the lateral view?
3. Describe and sketch the shape resulting from ach cross section.
a) b) c)
4. What is the name of a geometric solid that best describes the filing cabinet?
5. Based on what we’ve studied about prisms, identify two edges that are parallel and explain why.
11-1 Homework
Directions: Answer the following questions to the best of your ability. Show all work.
1) What types of solids are formed by a single translation?
2) Draw the base and lateral view for each figure.
3) What is the name of the following solid object? How could you form this solid using transformations?
4) The radius of the circle on the bottom is 10 cm. What is the area of the base of this cylinder to the nearest 10th?
5) The following cross sections were taken from a 3D solid. Figure 1 represents the
cross section perpendicular to the base, and figure 2 represents the cross section
parallel to the base.
What is the name of the solid that formed these cross sections?
Base Lateral Base Lateral
6.
6) A straw is placed into a rectangular box that is 3 inches by 4 inches by 8 inches, as shown in the accompanying
diagram. If the straw fits exactly into the box diagonally from the bottom left front corner to the top right back
corner, how long is the straw, to the nearest tenth of an inch?
7) Error Analysis! Brian is identifying the figure below. Find his mistake and correct it!
Brian say, “This figure has a rectangular base. It is a rectangular prism!”
7. For the following, sketch and name the solid that will match with the given cross section.
3D Figures Formed by Rotations
Today’s Goal: How are solid figures formed through rotations, and what are the properties?
Imagine this... You have a rectangular flag attached to a flagpole.
The wind blows so that the flag rotates all the way around the flagpole a full rotation.
What 3D figure would the "path" of the flag create?
Think about it! Yesterday we looked at solids formed by translations.
>>Circle which solids you think might be formed by a rotation?
>>What do each of these have in common?
Thinking in 3-D... with Rotations of Rectangles Google Sketch Up!
Sketch the 2D preimage Sketch the 3D figure formed when a rectangle is rotated into 3 dimensions.
Conclusion: when a rectangle is rotated into 3D, and we trace it’s path, a ____________ is formed.
Making Connections: The base view of a cylinder is a ___________________. The lateral view of a cylinder is a _____________________. The cross section parallel to the base is a _______________. The cross section perpendicular to the base is a ______________.
11-2 Notes
Thinking in 3-D... with Rotations of Right Triangles Google Sketch Up! Sketch the 2D preimage Sketch the 3D figure formed when a
rectangle is rotated into 3 dimensions.
Conclusion: when a triangle is rotated into 3D, and we trace it’s path, a ____________ is formed.
Making Connections: The base view of a cone is a ___________________. The lateral view of a cone is a _____________________. The cross section parallel to the base is a _______________. The cross section perpendicular to the base is a ______________.
All about Cones! A cone is... - a 3D solid figure with __________________________________________
Other Important Properties -________________ is the length from the center of base to the top
-_______________________________ is the length from the edge of the base to the top
Thinking in 3-D... with Rotations of Semi-Circles Google Sketch Up! Sketch the 2D preimage Sketch the 3D figure formed when a
rectangle is rotated into 3 dimensions.
Conclusion: when a semi-cirlce is rotated into 3D, and we trace it’s path, a ____________ is formed.
Making Connections: All views are a ______________________ All cross sections are ______________________
All about Spheres! A sphere is... -3D closed surface
-set of points _______________________________ to one center point -_______________________ is the distance from the center most point to the surface
When two cross sections are
equidistant to the center of the
sphere, the cross sections are ____________.
A half sphere is a ________________
Applying our Knowledge
1) A right triangular flag is attached to a pole. The flag spins around the pole.
a) What mathematical transformation best represents the situation?
b) What is the resulting solid that would be formed? 2) A sphere is "sliced" open. Imagine looking at the half sphere.
a) What would be the shape of the face of the half sphere?
b) What 3D figure would you get if you translated that shape (from part a) into three dimensions? 3)
a) What figure would be created if the triangle were rotated around the y-axis?
b) What is the radius of its base?
c) What figure would be created if the triangle were rotated around the x-axis.
d) What is the radius of its base? 4) Find the length of the slant height of the following cone.
5) Which figure can have the same cross section as a sphere?
1)
3)
2)
4)
6) If the rectangle below is continuously rotated about side w, which solid figure is formed? Sketch it!
11-2 Homework
Directions: Answer the following questions to the best of your ability. Show all work.
1) Fill in the following charts for each solid provided:
Cross Section Perpendicular to base
Cross section parallel to base
2) a) What is the name of the following solid object? How could you form this solid using a transformation?
b) Name one other solid that has a cross section shape in common with this figure.
3) The lateral faces of any prism are composed of
1) congruent isosceles triangles 3) congruent right triangles
2) rectangles 4) squares
4) What figure would be created if the semi-circle below were rotated around the x-axis? Draw it!
5) Use the following diagram below to answer each part:
a) What 3D solid would result from rotating this rectangle about side Q?
b) The height of the solid (include units): c) Radius of the base of the solid (include units): Diameter of the base of the solid (include units): d) What do you notice about the units? e) What should you be aware of moving forward in this unit?
6) A two-dimensional cross section is taken of a three-dimensional object. If this cross section is a triangle, what cannot be the three-dimensional object? (1) cone (2) pyramid (3) cylinder (4) rectangular prism
7) William is drawing pictures of cross sections of the right circular cone below.
Which drawing cannot be a cross section of a cone?
1) 2) 3) 4)
Volume of Prisms and Cylinders
Learning Goals: (1) What is volume and how do we find the volume of a prism and a cylinder?
(2) What is Cavalieri’s Principle?
Look back at your notes and recall with your shoulder buddies:
1. What type of transformation was used to create prisms?
2. What do we call the “pre-image” that is translated?
3. What shapes did we translate to create 3D figures?
Getting ready for today! Let’s Discuss how this translation is related to the formula for volume. Let’s use technology to help us visualize!
With your partner: Below you will see the 2D shape with an area of 10 𝑐𝑚2 that was translated into a prism.
The volume of the prism was calculated to be 50 𝑐𝑚3 . After our discussion, why does this make sense?
Volume : 50 𝑐𝑚3
Volume for Prisms or Cylinders
Where B is the AREA OF THE BASE (not the length of the base)
h is the height/depth of the prism/distance between the two bases
Example 1: Before we calculate!
a) What do we call this figure? b) What is its volume?
Example 2: Examine the solid below, what did we translate to form it?
11-3 Notes
What would be the volume of this cylinder to the nearest 10th? We should be thinking…
What is the base?
What is the area of the base?
Which is the height? How do recognize it in the diagram?
Equal Volumes and Cavalieri’s Theorem Let’s discuss again! Consider the two figures below:
Make a prediction! Do you think the two figures below can hold the same amount of fluid? Why or why not?
a)
b)
a) Did we translate to form both solids? b) What is the area of the base in figure a? b? what do we notice? d) How many layers of the circle bases do we have in each shape? (what is the height of the solid?) Let’s explore a bit further ……. Let’s go back to the two figures above looking at calculated volumes …
What do we notice here? Cylinder A) Cylinder B)
What factors contribute to this?
V = 𝜋r2h
= 𝜋(2)2(4)
=16𝜋 in3
V = 𝜋r2h
= 𝜋(2)2(4)
=16𝜋 in3
Cavalieri’s Principle: any two solids that …..
have the same area of the ____________ _____________ parallel to the base throughout the
height of the solid as well as the same ______________also have the same______________.
Example: Would Cavalier’s principle hold true here? Why?
Let’s think! Morgan tells you that Cavalieri’s principle cannot apply to the prisms shown below because their bases
are different. Do you agree or disagree? Explain.
Now let’s see how we can apply this theorem!
The diagram below shows two figures. Figure A is a right triangular prism and figure B is an oblique triangular
prism. The base of figure A has a height of 5 and a length of 8 and the height of prism A is 14. The base of
figure B has a height of 8 and a length of 5 and the height of prism B is 14.
Use Cavalieri's Principle to explain why the volumes of these two triangular prisms are equal.
r=4 r=4
Time to Practice These Skills! Work with your partners!
1)Find the volume of a rectangular prism with a length of 8 cm, a width of 10 cm, and a height of 4 cm. 2) Find the volume of a cube with an edge of 8 m. 3) Find the volume of the following triangular prism.
4) The volume of a rectangular pool is 1,080 cubic meters. Its length, width, and depth are in the ratio . Find the
number of meters in each of the three dimensions of the pool.
5) A box in the shape of a cube has a volume of 64 cubic inches. What is the length of a side of the box?
1) in 3) 8 in
2) 16 in 4) 4 in.
6) Consider a stack of square papers that is in the form a right prism.
a) What is the volume of the prism?
b) When you twist the stack of papers, as shown at the right, do you change the volumes Explain your reasoning.
c) Use your conjecture to find the volume of the twisted stack.
7) Reese has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. He
needs to build another rectangular prism with a length of 5 centimeters and the same height as the original prism. The
volume of the two prisms will be the same. Find the width, in centimeters, of the new prism.
Before you calculate, answer this!
If the volumes are equal and heights
are also equal, according to cavelieri’s
principle what else must be true?
Now let’s solve!
11-3 Homework
Directions: Answer all questions to the best of your ability.
1) If the area of the base of a triangular prism is 16in and the height is 20 in, find the volume.
2) Find the volume of the triangular prism.
3) Find the volume of a right circular cylinder with radius = 1.4m and height = 6m
a) in terms of
b) to the nearest cubic unit
4) A rectangular prism has an altitude of 12 inches and a base area of 32 inches. A second rectangular prism has a base
with length 7 in, an altitude of 12 in, and the same volume as the first prism. Find the width of the base to the
nearest tenth of an inch.
5) Each stack of memo papers contains 500 equally-sized sheets of paper. Compare their volumes. Explain your
reasoning.
6) The prisms described below have the same height as the prism shown. Which of the two prisms has the same
volume as this prism? Explain your reasoning.
Prism A: The base is a right triangle with legs 8 inches and 5 inches.
Prism B: The base is a square with side lengths of 4.5 inches.
7) A fish tank in the shape of a rectangular prism has dimensions of 14 inches, 16 inches, and 10 inches. The tank
contains 1680 cubic inches of water. What percent of the fish tank is empty?
8) Perfume is in a bottle in the shape of a cylinder with a diameter of 3 inches and a height of 4 inches. The
manufacturer would like to package a new cylindrical bottle of perfume with a diameter of 2 inches. What would
the height of the new bottle be to the nearest tenth of an inch, if the perfume bottles will have the same volume?
Check the key
and see
how you did!!
Volume of Pyramids, Cones and Spheres
Today’s Learning Goal: How do we find the volume of pyramids, cones and Spheres, and how are they related to other
volume formulas we have learned?
Volume of a Pyramid
Let's explore as a class...
Reactivate: How are prisms formed?
How do we find the volume of a prism?
Let's see how this relates to the volume of a pyramid! (video)
Try it with your shoulder buddy, what do you think the formula for pyramids might be?
11-4 Notes
Warm-up- With your shoulder buddy!
Solid Formed by what
transformation/s?
How many
Bases?
What is the measure of the
height?
Pyramid
Cone
Example 1: The diagram below is a regular pyramid. Find the volume of the pyramid to the nearest cubic unit.
What other solid could also be created by a dilation and translation?
Let’s try it!
Example 2: The diagram shows a cone of height 8 units and base radius 6 units. What is its volume in term of 𝜋 ?
Volume of a Pyramid:
Volume of a Cone:
The odd ball! :-)
Let's Try It!
What is the volume, to the nearest hundredth of a cubic inch, of a sphere with a radius of 5 inches?
Group Work!
Directions: In your groups, you will advance through three sections. The Stretch will help you practice the basics of volume.
In the Jog section, you will pick it a notch. In the sprint you will go full speed into a real-life application. Support each
other at every point!
Stretch
1) Find the volume of a pyramid if the base is a right triangle with legs of 8 inches and 10 inches, and the height of the
pyramid is 27 inches. Round to the nearest tenths.
2) Find the volume of the right circular cone to the nearest cubic foot.
Volume of a Sphere:
Jog
3. When Connie camps, she uses a tent that is in the form of a regular pyramid with a square base.
The length of an edge of the base is 9 feet and the height of the tent at its center is 8 feet. Find the
volume of the space enclosed by the tent to the nearest cubic foot.
4. A pharmacist is filling medicine capsules. The capsules are cylinders with half spheres on each end. If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold? (Round answer to the nearest tenth of a cubic mm.)
Sprint
5. The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is composed
of a hemisphere, a cylinder, and a cone. Let C be the center of the hemisphere and let D be the center of the base of the
cone.
If feet, feet, and , determine and state, to the nearest cubic foot, the volume of the water
tower.
11-4 Homework
Directions: Answer the following questions to the best of your ability. Show all work to receive full credit.
1) Find the volume of a cone to the nearest tenth with a radius of 8inches and a height of 20 inches.
2) The American Heritage Center at the University of Wyoming is a conical building. If the height is 77 feet, and the area
of the base is about 38,000 square feet, find the volume of air that the heating and cooling systems would have to
accommodate. Round to the nearest tenth.
3) Find the volume of a pyramid to the nearest cubic foot that has a square base with an edge of 2 feet, and the height
of the pyramid is 1.5 feet.
4) The volume of a pyramid is 576 cubic inches and the height of the pyramid is 18 inches. Find the area of the base to
the nearest squared inch.
6) If a golf ball has a diameter of 4.3 cm and a tennis ball has a diameter of 6.9cm, find the difference between the volumes of the 2 balls to the nearest tenth.
7) A right cone has a height of 6 feet and a volume of 32 cubic feet. What is its radius to the nearest foot?
8) A child’s toy is fully filled with a heavy liquid in the hemisphere and lighter liquids in the cone and cylinder so that the
toy will always right itself (stand up straight) as it is shown in the picture. The slant height of the cone is 10 in, height of
cylinder is 16 in and the radius is 6. How much total liquid is contained inside of the toy to the nearest tenth?
𝑙 = 10𝑖𝑛
16 in
6 IN
Today’s Goal: How can we apply volume to real-life modeling problems?
Today we are going to be looking at real-life “models” that require the knowledge of solids and its applications.
In your teams:
1. Read the problem, highlight/annotate any key words are pieces of information
2. Come up with a plan! Write any ideas, solve for anything you CAN solve for and reason through how you’ll get your answer!
Model 1) A shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 8.5 feet,
and a height of 4 feet. The container is completely filled with contents that weigh, on average, 0.25 pounds per cubic
foot. What is the weight, in pounds, of the contents in the container?
What’s our method?
Let’s Try it!
3. Think you have model #1? Check in with your teacher, then try model #2
Model 2) A hemispherical tank is filled with water and has a diameter of 10 feet. If water weighs 62.4 pounds per cubic
foot, what is the total weight of the water in a full tank, to the nearest pound?
SHOW WORK TO SUPPORT YOUR ANSWER CHOICE. Be prepared to explain yourself!
1) 16,336
2) 32,673
3) 130,690
4) 261,381
11-5 Notes
DENSITY APPLICATIONS
There are 2 types of scenarios we encounter that deal with DENSITY In Geometry we look at both scenarios!
Today: Population Density -a ratio of the amount of a population that exists over a given area
Next Lesson: Density of a 3D Solid -a ratio that compares an object’s weight (mass) to the amount of space (volume) it takes up
Let’s take a look at population density first!
The diagram below shows two towns: Lollipop and West Lollipop. Each dot plotted in their area represents 20
individuals who live in that region. Which town do you think has a greater population density? Justify your answer.
Model 3) During an experiment, the same type of bacteria is grown in two petri dishes. Petri dish A has a diameter of 51
mm and has approximately 40,000 bacteria after 1 hour. Petri dish B has a diameter of 75 mm and has approximately
72,000 bacteria after 1 hour.
Determine and state which petri dish has the greater population density of bacteria at the end of the first hour.
Population density =
11-5 Practice and Homework 1. Last Class, we saw the water tower problem. The water tower in the picture below is modeled by the two-dimensional
figure beside it. The water tower is composed of a hemisphere, a
cylinder, and a cone.
Here we were able to determine that the volume of the water tower is
7650 ft3.
Question: The water tower was constructed to hold a maximum of
400,000 pounds of water. If water weighs 62.4 pounds per cubic foot, can
the water tower be filled to 85% of its volume and not exceed the weight
limit? Justify your answer.
2. Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere
weighs .075 pound per cubic inch. If the sphere's radius is 4 inches, what is the weight of the sphere, to the nearest
pound?
1) 34
2) 20
3) 15
4) 4
3. Walter wants to make 100 candles in the shape of a cone for his new candle business. The mold shown right will be
used to make the candles.
a) Each mold will have a height of 8 inches and a diameter of 3 inches. To the nearest cubic
inch, what will be the total volume of 100 candles?
b) Walter goes to a hobby store to buy the wax for his candles. The wax costs $0.10 per ounce. If the weight of
the wax is 0.52 ounce per cubic inch, how much will it cost Walter to buy the wax for 100 candles?
c) If Walter spent a total of $37.83 for the molds and charges $1.95 for each candle, what is Walter's profit
after selling 100 candles?
4. The population density of Huskyville is 17.5 Huskyvillers per acre. Exactly 840 Huskyvillers live in Huskyville.
How many acres does Huskyville cover?
5. As of 2015 the most densely populated state in the US was New Jersey. The 2015 population of NJ was 8,957,907
people with 1218.1 people per square mile. Which choice is the approximate land area of the state of NJ to the
nearest square mile?
a. 7,135 square miles
b. 10,912 square miles
c. 7354 square miles
d. 12354 square miles
6. Log On to GOOGLE Classroom fill out today’s Form 11-5!
7. Complete today’s Looking Forward Question
8. Fill in the following:
a. Write all 2 solids formed by a translation and dilation:
b. What 3 solids have a cross section that is a circle?
c. What solid has a circular base and is formed by a translation?
d. What solid has a cross section parallel to the base of a triangle, and a cross section perpendicular to the base of a
rectangle?
e. What solid would have any cross section produce a circle?
Today’s Goal: How can we apply volume to real-life modeling problems?
Last Class: Population Density -a ratio of the amount of a population that exists over a given area
Today: Density of a 3D Solid -a ratio that compares an object’s weight (mass) to the amount of space (volume) it takes up
To calculate the Density of a solid we use the following formula
BE CAREFUL!
Tips for Density of Solid Problems:
*SOMETIMES YOU MUST CONVERT UNITS BEFORE STARTING THE PROBLEM
*If you can calculate volume in the problem, do that first!
Model 1) A wooden cube has an edge length of 6 centimeters and a mass of 137.8 grams. Determine the density of the
cube, to the nearest thousandth. State which type of wood the cube is made of, using the
density table below.
Before we proceed let’s Reactivate: Conversions:
Convert the following:
5.1 cm = ___________ meters
10.2 cm = ___________ meters
20.3 cm = ___________ meters
11-6 Notes
Model 2) A contractor needs to purchase 500 bricks. The dimensions of each brick are 5.1 cm by 10.2 cm by 20.3 cm,
and the density of each brick is . The maximum capacity of the contractor’s trailer is 900 kg. Can the trailer
hold the weight of 500 bricks? Justify your answer.
a) Notice how density is given in kilograms per meters cubed? 1st convert dimensions of the brick so it’s in meters too!
b) Now volume of a brick.(Keep the long decimal)!
c) Fill into density formula; find the mass (weight) of one brick.
d) Can the trailer hold 500 bricks? Justify your answer!
We are practicing! Complete the following problems, and the EdPuzzle! Check in Quiz Before Review in Class!
1. A cube has edges of 6cm and a density of 10 g/cm3.What is the mass of the cube?
2. Danielle has a full container of ice cream which has a density of 0.1 pounds per cubic inch. The container is a sphere
which has a radius of 3 inches. Marisa also has a full container of ice cream, which has a density of 0.01 pounds per
cubic inch and is contained in a sphere which has a radius of 3 inches.
How many more pounds of ice cream does Danielle have than Marisa (ie, the difference)? Round any decimals to the
nearest hundredth at the end of the problem.
3. A hot air balloon holds 74,000 cubic meters of helium, a very noble gas with the density of 0.1785 kilograms per
cubic meter. How many kilograms of helium does the balloon contain?
4. The Property Brothers remodeled a kitchen and installed granite countertops.
A rectangular island in the kitchen now has a granite top measuring 5ft by 8
ft. by 1.2 inches. The density of granite is 2.7 g/in3.
How many grams is the weight of the island to the nearest tenth?
5. The HHS Math Talent show is giving out cylinder trophies this year to its winners. The trophy is a cylinder with a
height of 18 cm and a radius of 6 cm. The density of gold is 19.32 g/cm3 and the density of silver is
10.5 g/cm3.
How much heavier is the gold trophy compared to the silver to the nearest whole gram?
6. Begin Flipped Video Lesson (prep for tomorrow)
Ready? Scenario:
It will take 2400 cubic inches of packing peanuts to fit in the following box.
It will take 1120 square inches of wrapping paper to cover the box (Without any overlap)
a) What information tells you about the volume of this box?
b) What information tells you about the surface area of this box?
c) What is surface area?
Surface Area
The surface area of a 3-Dimensional solid is... Here’s an example:
Find the surface area of a rectangular prism whose length is 6 meters, width is 4 meters, and height is 5.
Still unsure? Watch the video again! Complete next page; be prepared for a check in!
7. The rectangular prism shown below has a length of 3.0 cm, a width of 2.2 cm, and a height of 7.5 cm.
What is the surface area, in square centimeters?
8. Mr. Roberts is painting the outside of his son’s toy box, including the top and bottom. The toy box measures 3
feet long, 1.5 feet wide, and 2 feet high. What is the total surface area he will paint? (Hint: Draw the figure and
it’s net! OR remember our shortcut for rectangular prisms!)
You choose! Complete ONE of the following two problems, the right column is more of a challenge!
9. How many square inches of wrapping paper are
needed to entirely cover a box that is 2 ft by 3 ft by 6
ft?
9. Find the surface area of the figure below. Remember draw
and label the “net!!”
