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Detailed Lesson PlanInMathematics(Geometry)

I. OBJECTIVES:At the end of the lesson the students are expected to:a. derive formulas for the surface areas and volumes of solid figures; andb. solve problems involving the surface areas and volumes of solid figures.

II. CONTENT and MATERIALS:

a. Content: Surface Area and Volumeb. Materials: Chalk, Chalkboard, Visual Materials (Solid Figures), Cartolina, Manila Paper, Laptop and LCD (if available) and Calculator (if needed).c. Reference: New High school Mathematics III (Second Edition)

III. PROCEDURE/ DEVELOPMENT OF THE LESSON

a. Motivation

TEACHERS ACTIVITYSTUDENTS ACTIVITY

Good Morning Class!Good Morning Sir

Can you see the things on my desk?Yes Sir!

Can you recognize them?Yes Sir, they are solid figures or three dimensional figures, naming it from left to right thats a CUBE, RECTANGULAR PRISM, PYRAMID, CONE, CYLINDER and SPHERE.

Very good Ivan!

Look around, Can you see solid figures?Yes Sir, the Eraser, Chalk box and your table top are examples of rectangular prism

Thats very good observation Jerome!

Sir, the ice cream in a cone which I bought during recess time is an example of cone.

Sir, the pencil holder in your desk is an example of Cylinder.

Very good Misty!

Those are just few of many examples of solidFigures

b. Presentation

Today we will be measuring the volume andsurface area of each solid figure.(Students Listens)

Lets start by differentiating VOLUME from SURFACE AREAWhat is VOLUME?Sir, Volume is the amount of space occupied by a solid figure.Very good Ellen!

How about SURFACE AREA?Sir, the surface area is the sum of the areas of faces of a solid figure.

Very good James!

To illustrate the difference, I have here a soft drink in a can, if we talked about VOLUME of this can Im talking about the soda inside, while (Students Listens)SURFACE AREA is the sheet metal used in theconstruction of this can.

Is it clear class?Yes Sir!

CUBE

(the teacher will let the students hold and observe the sample figure)

What solid is this?Sir, its a CUBE

What special features do you observed with theSir, it has six (6) square faces.figure?

Very good Norma!

Since it has 6 faces (square), we can solve its surface area by finding the sum of this faces.

Scube= 6s2Sir, I will trySolving for surface area: Scube= 6s2 Scube= 6(5)2 Scube= 6(25) Scube= 150 square inchers

Solving for volume:

VCUBE= s3 VCUBE= 53 VCUBE= 125 cubic inches

where s are the measure of the side of squareor cube.

Thus, to solve for its volume, we multiply the threedimension of this solid

VCUBE= s3

Lets have an example, find the volume andsurface area of the figure below.5 inches

Who wants solve the problem?

Very Good Stella!RECTANGULAR PRISMHeightLengthwidth

According to Jerome a while ago, ERASER, BOOK and my TABLETOP are the best representation ofthis figure, the RECTANGULAR PRISM.(Students Listen)(the teacher will let the students hold the figure)

What special feature do you observed with theSir, I observed that the faces of thefigure?rectangular prism are congruent and parallelSir, I also observed that the opposite faces of the rectangular prism are congruentand parallelBoth of you are correct. Using this property we canmeasure its surface area by getting all the area offaces (rectangle), thus

SRECTANGULAR PRISM=

While for its volume, we multiply the three dimen-(Students Listen)sion, thus

VRECTANGULAR PRISM=

Any question with the formula?None Sir!

So lets have thus example:

A rectangular prism has the following dimen-sions 8 by 2 by 4 inches respectively. Find the volume and surface area.

Who wants to solve?Solving for surface area:SRECTANGULAR PRISM= SRECTANGULAR PRISM= SRECTANGULAR PRISM= SRECTANGULAR PRISM= 112 square inches

Solving for its volume:VRECTANGULAR PRISM= VRECTANGULAR PRISM= VRECTANGULAR PRISM=

Thats correct! Very good Nicole.PYRAMID

Height

Slant HeightLengthWidth

Have you heard, read or seen in television aboutthe Egyptian Pyramids?Yes Sir!

I have here a sample figure of pyramid(the teacher will let the student hold and observethe figure)

Describe it!Sir, the faces of pyramid except the base, areTriangles.

I also notice that the triangular face of the py-ramid meet at a common point.That was very good observation Alvin!

TAKE NOTE: the base of a pyramid can be a diffe-rent sided polygon. A pyramid is named according(Students Listens)to its base. A pyramid may be triangular, square, orpentagonal depending on its base

Using its properties, we can find the surface area ofa pyramid by adding the area of the base to thesum of the areas of all triangular faces.

SPYRAMID=

where; B= area of basen= number of triangular facess= length of sidel= slant height(Students Listens)

and for its volume

VPYRAMID=

where; B= area of baseh= height

Any question with the formula class?None Sir!

Then lets try and solve the figure in the board

8 cm3 cm5 cm

Who wants to solve the volume and surface area?Sir, I would like to try!For its surface area:SPYRAMID= SPYRAMID= SPYRAMID= SPYRAMID= and for its volume:VPYRAMID= VPYRAMID= VPYRAMID= VPYRAMID= VPYRAMID= 64 cubic inches

Very Good Vic!

CONEradiusHeightslant height

(the teacher let the student hold and observe the figure)

Did you notice that the base is circle?Yes Sir!

A cone is a solid figure with a vertex and a circularbase.(Students Listens)

To solve for its SURFACE AREA of the cone we needto find the sum of the lateral area and circular base(see figure)

SCONE=

where: l= slant height(Students Listens)r= radius

And to solve for the volume of the cone, we use;

VCONE =

where: r= radiush= height = 3.14

Lets have an example, the figure on the board is acone with measures of its parts.Sir, I will try

Solving for the surface area of the cone

SCONE= SCONE= SCONE

Solving for the volume of the cone

VCONE = VCONE = VCONE

5 cm.4 cm.7.21 cm.

Very Good Sonny!

CYLINDER

radiusHeight

Another solid figure is a cylinder (the teacher will letthe students hold and observe the figure)

What significant features you can observe in that Sir, it has parallel and congruent circularfigure?bases.

Very Good Toni!

To solve for the surface area, we rolled out the cylin-der.

What can you notice?Sir, I can see two circles and a rectangle

thats correct!

Thus, to solve for its surface area we need to find thesum of the area of rectangle and 2 circles.

SCYLINDER= ARECTANGLE + 2 ACIRCLESCYLINDER=

since l= circumference of circle = andw=height of the circle, we rewrite the formula as(Students Listens)

SCYLINDER=

and to solve for its volume, we use the formula:

VCYLINDER=

Any question with the formula class?None Sir!

Lets try this example. Find the volume and surfaceSir, I will solve for the volume and surface area

SCYLINDER= SCYLINDER= SCYLINDER= SCYLINDER

Volume:

VCYLINDER= VCYLINDER= (3.14)VCYLINDER=

area of the solid5 cm.2 cm.

Very Good Samuel!

SPHEREr

Another solid which we find very common in our every-day life is the sphere

(the teacher will let the student hold and observe thefigure)

For us to measure the surface area of the sphere, we (Students Listens)use the formula

SSPHERE=

and for volume

VSPHERE=

where r is the radius of sphere

c. Activity/ Application

Its time to apply our learnings in finding volume andsurface area.

The class will be divided (3 or more groups)(Student will group themselves)Task: Find the volume and surface area of the things/objects assigned to the group.

Class, before we start assign first your leader and secre-tary

(Every group will be given a maximum of 10 minutesin solving their respective objects and a maximum of (Student will proceed to their5 minutes for the reporting of results)respective groups and willparticipate)Items included are the following: Golf ball, Marble, Junior ball Dice, Toy cube ring box, gift box, cellphone box softdrink can, empty can good in different sizes cone (ice cream) model of a pyramid

Note: Each item has an attached paper where the values necessary for solving surface area and its(Students Listens)volume are given.

(The teacher will roam around to make sure that activi-ties are being followed and to answer inquiries orclarifications related to the activity)

(After the activity, a participant of the group will reporttheir solution in front of the class)

(result of each group will be submitted to the teacherafter the activity)

d. Summary

A space figure or three dimensional solid figure has faces, edges, and vertices The surface area S is the sum of the area of its faces The volume V of a solid is the number of cubic units contained in it.Cube: Scube= 6s2 and VCUBE= s3

Prism (rectangular): SRECTANGULAR PRISM= and VRECTANGULAR PRISM=

Cylinder: SCYLINDER= and VCYLINDER=

Pyramid: SPYRAMID= and VPYRAMID=

Cone: SCONE= and VCONE =

Sphere: SSPHERE= and VSPHERE=

IV. EVALUATION

Direction: Solve the following(Answer Key)

1. A sewing box has the dimension 10 cm by 8 cmV= 10 x 8 x 5 by 5 cm. What is its volume?V= 400 cubic centimeter

2. A cylindrical tank has a radius of 1.5 cm and a height of 8 cm

a. How much material was used making it?a. SCYLINDER= b. determine how much water the tank containsSCYLINDER= SCYLINDER

b. VCYLINDER= VCYLINDER= VCYLINDER

3. The base of a rectangular pyramid is 8 cm by 10cm. If its height and slant height are 12 cm and 3. VPYRAMID= 15 cm respectively, what is its volume?VPYRAMID=

VPYRAMID= IV. ASSIGNMENT

Direction: Solve the problem below ( Use the figurebelow)

2 cm

2 cm2 cm2 cm

1. A piece of cardboard, whose length is 20 cm andwhose width is 10 cm, is folded on the dotted linesto make an OPEN box. Find the following

a. Height of the boxa. 2 centimeters

b. Surface area of the open boxb. Since it is an OPEN box, one of its face is notmultiplied by 2.S= 2(2)(16) + 2(2)(6) + 16(6)S= 184 square centimeters

c. Volume of the boxc. V= l x wx hV= (2)(16)(6)V= 192 cubic centimeters

Prepared by:

Jeffreynald A. Francisco