develop skills and strategies lesso 24 part 1 introduction ... · 2 an artist is commissioned to...

©Curriculum Associates, LLC Copying is not permitted.L24: Surface Area of Solids228

Surface Area of SolidsLesson 24 Part 1: Introduction

In grade 6, you learned to use nets to represent rectangular prisms. In this lesson, you will learn to find surface area of rectangular prisms and other right prisms.

Find the surface area of the building block in Ben’s construction set shown below.

4 in.

1 in.

2 in.

Explore It

Use the math you already know to solve the problem.

How many faces does the block have? What shape are the faces?

Draw the top and bottom faces and label their dimensions

Draw the front and back faces of the block and label their dimensions

Draw the side faces and label their dimensions

How could you find the surface area of the block?

Develop Skills and Strategies

CCLS7.G.B.6

©Curriculum Associates, LLC Copying is not permitted.229L24: Surface Area of Solids

Lesson 24Part 1: Introduction

Find Out More

The surface area of a three-dimensional figure is the sum of the areas of all its faces A rectangular prism has three pairs of faces that are the same size and shape

wl

h

The top and bottom faces have the same area: A 5 lw

The front and back faces have the same area: A 5 hw

The left and right side faces have the same area: A 5 hl

To find the surface area of a rectangular prism, add the areas of all six faces

Surface Area 5 lw 1 lw 1 hw 1 hw 1 hl 1 hl

top bottom front back left side right side

5 2lw 1 2hw 1 2hl

Reflect

1 How can you find the surface of area of a cube with edge length 3 in ?

Lesson 24

©Curriculum Associates, LLC Copying is not permitted.

L24: Surface Area of Solids230

Part 2: Modeled Instruction

Read the problem below. Then explore different ways to calculate the surface area of a triangular prism.

How many square feet of nylon fabric would be needed to make the camping tent shown below?

8 ft

6 ft

4 ft5 ft5 ft

Picture It

You can draw and label the dimensions of the five faces of this prism.

The tent is in the shape of a right triangular prism The bases of the prism are two triangles that are the same size and shape

6 ft

4 ft

5 ft5 ft

6 ft

4 ft

5 ft5 ft

The other faces of the prism are three rectangles:

8 ft

6 ft

8 ft

5 ft

8 ft

5 ft

Solve It

You can use formulas to find the areas of the faces.

Area of a rectangle with length, l, and width, w:

A 5 lw

Area of a triangle with base, b, and height, h:

A 5 1 ·· 2 bh

Lesson 24


Part 2: Guided Instruction

Connect It

Now you will use the model and formulas to find the surface area and solve the problem.

2 How can you find the areas of the faces of the prism?

3 Do you have to find the areas of five different figures? Explain your thinking

4 What is the area of a triangular base? Show your work

5 What are the areas of the rectangular faces? Show your work

6 How could you find the surface area of the tent?

7 Use your own words to explain how to find the surface area of a right triangular prism

Try It

Use what you just learned about finding the surface area of a triangular prism to solve the following problems. Show your work on a separate sheet of paper.

8 Find the surface area of the prism

9 Suppose a cube has the same surface area as the prism in problem 8 Find the edge length of the cube

7

6

10

8

Lesson 24



Read the problem below. Then use what you learned about calculating surface areas of prisms to solve the problem.

Mrs. Anderson wants to buy a glass greenhouse with the dimensions shown. The greenhouse will not have a floor. What is its surface area?

Picture It

You can draw and label the dimensions of the faces of this prism.

6.5 ft6.5 ft8 ft8 ft12 ft12 ft

15 ft15 ft15 ft15 ft8 ft8 ft

6.5 ft 6.5 ft

10.5 ft 10.5 ft

Model It

You can find the area of one of the bases by breaking into a rectangle and a triangle.

12 ft

8 ft

6.5 ft 2.5 ft

Solve It

You can use formulas to find the area of each of the faces.

Area of a rectangle with length, l, and width, w:

A 5 lw

Area of a triangle with base, b, and height, h:

A 5 1 ·· 2 bh

Part 3: Modeled Instruction

12 ft

8 ft

6.5 ft

15 ft

10.5 ft

Lesson 24


Connect It

Now you will use the models and formulas to find the surface area of the greenhouse.

10 Look at Model It How do you know that the height of the triangle is 2 5 ft?

11 What is the area of one of the bases of the prism? Show your work and explain your reasoning

12 Describe the other faces of the prism, including their dimensions

13 What is the surface area of the greenhouse? Show your work

14 Explain how to find the surface area of any right prism

Try It

Use what you just learned about calculating surface area to solve the problem below. Show your work on a separate sheet of paper.

15 Find the surface area the prism shown below Include all faces, even the bottom

30

20

8

120

17

Part 3: Guided Instruction

Student Model

Part 4: Guided Practice Lesson 24



Study the model below. Then solve problems 16–18.

Jing put two identical building blocks on top of each other. The dimensions of each block were 2 in. by 2 in. by 4 in. What is the surface area of the resulting prism?

Look at how you could show your work by drawing a model.

There are 4 faces that are 2 in. by 8 in. and 2 faces that are 2 in. by 2 in.

Surface Area 5 4(2)(8) 1 2(2)(2) 5 64 1 8

Solution:

16 Find the surface area of the prism shown below

12 cm8 cm4 cm

5 cm 5 cm6 cm

Show your work.

Solution:

72 sq in.

Why can’t you find the surface area of each block and double it?

Pair/Share

The student found the dimensions of the new figure and found its surface area.

What information do you need to find the surface area of any prism?

Pair/Share

How many faces does this prism have?

4 in.

4 in.

2 in.2 in.

Part 4: Guided Practice Lesson 24


17 How much wrapping paper would you need to cover a rectangular box that is 19 inches by 12 inches by 3 inches if you need 10% more wrapping paper than the surface area of the box? Give your answer to the nearest square inch

Show your work.

Solution:

18 Find the surface area of the solid below Circle the letter of the correct answer

A 32 5 sq cm

B 210 sq cm

C 225 sq cm

D 240 sq cm

Alex choose D as the correct answer What did she do wrong?

How could you check to see if your answer is reasonable?

Pair/Share

Would drawing a model help?

Can you think about this as one solid figure?

Pair/Share

What two solids make up this three-dimensional figure?

6 in.

10 in.8 in.

6 in. 2 in.12

Lesson 24



Solve the problems.

1 Two cubes with edge lengths of 3 centimeters and 2 centimeters are placed on top of each other as shown. What is the surface area of the resulting figure?

A 65 cm C 74 cm

B 70 cm D 78 cm

2 An artist is commissioned to build two hollow glass sculptures standing vertically, one in the form of a triangular prism and one in the form of a rectangular prism. Their dimensions are shown below.

[not drawn to scale]

SCULPTURE 2SCULPTURE 1

12 in.

5 in.5 in.

17 in.

6 in.

4 in.

5 in.5 in.

Choose True or False for each statement.

A The volume of Sculpture 1 is greater than the volume of Sculpture 2. True False

B The surface area of Sculpture 2 is less than the surface area of Sculpture 1. True False

C The base of Sculpture 1 covers a larger area than the base of Sculpture 2. True False

D Sculpture 1 requires more glass to complete than Sculpture 2. True False

Part 5: Common Core Practice

Lesson 24


3 The prism below has dimensions 2 inches by 3 inches by 4 inches. To the right of the prism, shade the number of prisms necessary, if stacked on top of each other as shown, to create a new prism with a surface area between 100 square inches and 130 square inches.

2 in.

3 in.4 in.

4 Mario’s father is building a skateboard ramp in the shape of a triangular prism. Mario has agreed to paint the ramp once it’s finished. If a quart of paint covers 85 square feet, how much paint will Mario need to buy? (Mario doesn’t have to paint the bottom of the ramp.)

7 ft10.5 ft

24 ft

25 ft

Show your work.

Answer Mario needs to buy quarts of paint.

Go back and see what you can check off on the Self Check on page 169.Self Check

Part 5: Common Core Practice

develop skills and strategies lesso 24 part 1 introduction ... · 2 an artist is commissioned to...

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