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In this pdf we will be finding surface area of composite solids. A composite solid is made up of two or more solid figures. To find the surface area of a composite solid, find the surface area of each figure.

1.
English Spanish

6.6 Surface Areas of Composite Solids

How can you find the

S

STATE surface area of a composite solid?

STANDARDS

MA.7.G.2.2

1 ACTIVITY: Finding a Surface Area

Work with a partner. You are manufacturing scale models of old houses.

a. Name the four basic

solids of this

Front View

composite figure. 18 in.

b. Determine a strategy for

finding the surface area

of this model. Would

you use a scale drawing?

Would you use a net?

Explain.

60 in.

36 in. 16 in.

Many castles have cylindrical

towers with conical roofs.

These are called turrets.

36 in.

24 in.

Top View

282 Chapter 6 Surface Areas of Solids

6.6 Surface Areas of Composite Solids

How can you find the

S

STATE surface area of a composite solid?

STANDARDS

MA.7.G.2.2

1 ACTIVITY: Finding a Surface Area

Work with a partner. You are manufacturing scale models of old houses.

a. Name the four basic

solids of this

Front View

composite figure. 18 in.

b. Determine a strategy for

finding the surface area

of this model. Would

you use a scale drawing?

Would you use a net?

Explain.

60 in.

36 in. 16 in.

Many castles have cylindrical

towers with conical roofs.

These are called turrets.

36 in.

24 in.

Top View

282 Chapter 6 Surface Areas of Solids

2.
English Spanish

2 ACTIVITY: Finding and Using a Pattern

Work with a partner.

● Find the surface area of each figure.

● Use a table to organize your results.

● Describe the pattern in the table.

● Use the pattern to find the surface area of the figure

that has a base of 10 blocks.

3 ACTIVITY: Finding and Using a Pattern

Work with a partner. You own a roofing company. Each building has the

same base area. Which roof would be cheapest? Which would be the most

expensive? Explain your reasoning.

flat lean-to gable hip

cross-hipped gambrel mansard cross-gabled

4. IN YOUR OWN WORDS How can you find the surface area of a

composite solid?

5. Design a building that has a turret and also has a mansard roof.

Find the surface area of the roof.

Use what you learned about the surface area of a composite solid

to complete Exercises 6 – 8 on page 286.

Section 6.6 Surface Areas of Composite Solids 283

2 ACTIVITY: Finding and Using a Pattern

Work with a partner.

● Find the surface area of each figure.

● Use a table to organize your results.

● Describe the pattern in the table.

● Use the pattern to find the surface area of the figure

that has a base of 10 blocks.

3 ACTIVITY: Finding and Using a Pattern

Work with a partner. You own a roofing company. Each building has the

same base area. Which roof would be cheapest? Which would be the most

expensive? Explain your reasoning.

flat lean-to gable hip

cross-hipped gambrel mansard cross-gabled

4. IN YOUR OWN WORDS How can you find the surface area of a

composite solid?

5. Design a building that has a turret and also has a mansard roof.

Find the surface area of the roof.

Use what you learned about the surface area of a composite solid

to complete Exercises 6 – 8 on page 286.

Section 6.6 Surface Areas of Composite Solids 283

3.
English Spanish

6.6 Lesson

Lesson Tutorials

Key Vocabulary A composite solid is a figure that is made up of more than one solid.

composite solid, cone

cylinder

p. 284

composite solid

EXAMPLE 1 Identifying Solids

Identify the solids that make up Fort Matanzas, Florida.

Rectangular

prism

Cylinder

Approximately a

rectangular prism

EXAMPLE 2 Standardized Test Practice

You painted the steps to an apartment green. What is the surface area

that you painted?

20 in. 7 in.

10 in. A 210 in.2

○ B 408 in.2

○ ○

C 648 in.2 D 1056 in.2

○

7 in.

Find the area of each green face.

24 in.

Green area on top step:

20 in. A = 20(24) + 7(24) = 648 in.2

24 in. 7 in.

10 in. Green area on bottom step:

7 in. A = 10(24) + 7(24) = 408 in.2

24 in.

You painted 648 + 408 = 1056 square inches.

The correct answer is ○

D .

1. WHAT IF? In Example 2, you also painted the sides of the

Exercises 3–5 steps green. What is the surface area that you painted?

284 Chapter 6 Surface Areas of Solids

6.6 Lesson

Lesson Tutorials

Key Vocabulary A composite solid is a figure that is made up of more than one solid.

composite solid, cone

cylinder

p. 284

composite solid

EXAMPLE 1 Identifying Solids

Identify the solids that make up Fort Matanzas, Florida.

Rectangular

prism

Cylinder

Approximately a

rectangular prism

EXAMPLE 2 Standardized Test Practice

You painted the steps to an apartment green. What is the surface area

that you painted?

20 in. 7 in.

10 in. A 210 in.2

○ B 408 in.2

○ ○

C 648 in.2 D 1056 in.2

○

7 in.

Find the area of each green face.

24 in.

Green area on top step:

20 in. A = 20(24) + 7(24) = 648 in.2

24 in. 7 in.

10 in. Green area on bottom step:

7 in. A = 10(24) + 7(24) = 408 in.2

24 in.

You painted 648 + 408 = 1056 square inches.

The correct answer is ○

D .

1. WHAT IF? In Example 2, you also painted the sides of the

Exercises 3–5 steps green. What is the surface area that you painted?

284 Chapter 6 Surface Areas of Solids

4.
English Spanish

EXAMPLE 3 Finding the Surface Area of a Composite Solid

Find the surface area of the composite solid.

8m

The solid is made up of a square prism and a

square pyramid. Use the surface area formulas

for a prism and a pyramid, but do not include

4m

the areas of the sides that overlap.

6m

8m

6m

Do not include the top base of

the prism in the surface area.

4m

6m

6m

6m Do not include the base of the

6m

pyramid in the surface area.

Square prism

S = ℓw + 2ℓh + 2wh Write formula.

= 6(6) + 2(6)(4) + 2(6)(4) Substitute.

= 36 + 48 + 48 Multiply.

= 132 Add.

Square pyramid

S = areas of lateral faces Write formula.

(

=4 — 6 8

1

2 ⋅ ⋅ ) Substitute.

= 96 Multiply.

Find the sum of the surface areas: 132 + 96 = 228.

The surface area is 228 square meters.

Identify the solids that make up the composite solid. Then find

Exercises 6–11 the surface area. Round your answer to the nearest tenth.

2. 3.

5 yd

3 yd 4 cm

5 cm

5 yd

3 cm

5 cm

3 cm

Section 6.6 Surface Areas of Composite Solids 285

EXAMPLE 3 Finding the Surface Area of a Composite Solid

Find the surface area of the composite solid.

8m

The solid is made up of a square prism and a

square pyramid. Use the surface area formulas

for a prism and a pyramid, but do not include

4m

the areas of the sides that overlap.

6m

8m

6m

Do not include the top base of

the prism in the surface area.

4m

6m

6m

6m Do not include the base of the

6m

pyramid in the surface area.

Square prism

S = ℓw + 2ℓh + 2wh Write formula.

= 6(6) + 2(6)(4) + 2(6)(4) Substitute.

= 36 + 48 + 48 Multiply.

= 132 Add.

Square pyramid

S = areas of lateral faces Write formula.

(

=4 — 6 8

1

2 ⋅ ⋅ ) Substitute.

= 96 Multiply.

Find the sum of the surface areas: 132 + 96 = 228.

The surface area is 228 square meters.

Identify the solids that make up the composite solid. Then find

Exercises 6–11 the surface area. Round your answer to the nearest tenth.

2. 3.

5 yd

3 yd 4 cm

5 cm

5 yd

3 cm

5 cm

3 cm

Section 6.6 Surface Areas of Composite Solids 285

5.
English Spanish

6.6 Exercises

Help with Homework

1. OPEN-ENDED Draw a composite solid formed by a 7 in.

triangular prism and a cone.

2. REASONING Explain how to find the surface area of 10 in.

the composite solid.

4 in.

6)=3

9+(- 3)=

3+(- 9)=

4+(- =

1)

9+(-

Identify the solids that form the composite solid.

1 3. 4. 5.

Identify the solids that form the composite solid. Then find the surface area.

Round your answer to the nearest tenth.

2 3 6. 4 ft 7. 8m 8. 4 in.

8m

3 ft 4 in.

4m

10 m

6 ft

5 in.

6 ft

5 in.

5 in.

8 in.

9. 2 cm 10. 7 in. 11.

2.5 cm 8 ft

2 ft

2.5 cm 2 cm 8 in.

10 in.

3 cm 4 ft

6 cm 5 ft

5 cm 12 ft

8 in.

6.9 in.

12. OPEN-ENDED The solid is made using eight cubes

with side lengths of 1 centimeter.

a. Draw a new solid using eight cubes that has a

surface area less than that of the original solid.

b. Draw a new solid using eight cubes that has

a surface area greater than that of the original solid.

286 Chapter 6 Surface Areas of Solids

6.6 Exercises

Help with Homework

1. OPEN-ENDED Draw a composite solid formed by a 7 in.

triangular prism and a cone.

2. REASONING Explain how to find the surface area of 10 in.

the composite solid.

4 in.

6)=3

9+(- 3)=

3+(- 9)=

4+(- =

1)

9+(-

Identify the solids that form the composite solid.

1 3. 4. 5.

Identify the solids that form the composite solid. Then find the surface area.

Round your answer to the nearest tenth.

2 3 6. 4 ft 7. 8m 8. 4 in.

8m

3 ft 4 in.

4m

10 m

6 ft

5 in.

6 ft

5 in.

5 in.

8 in.

9. 2 cm 10. 7 in. 11.

2.5 cm 8 ft

2 ft

2.5 cm 2 cm 8 in.

10 in.

3 cm 4 ft

6 cm 5 ft

5 cm 12 ft

8 in.

6.9 in.

12. OPEN-ENDED The solid is made using eight cubes

with side lengths of 1 centimeter.

a. Draw a new solid using eight cubes that has a

surface area less than that of the original solid.

b. Draw a new solid using eight cubes that has

a surface area greater than that of the original solid.

286 Chapter 6 Surface Areas of Solids

6.
English Spanish

13. BATTERIES What is the percent increase in the surface area of the AAA battery

to the AA battery? Round your answer to the nearest tenth of a percent.

AAA battery AA battery

0.8 mm 1 mm

43 mm

3.8 mm 49 mm 5.5 mm

10 mm

14 mm

1.75 in. 5 in. 14. BARBELL The diameter of the handle of a barbell is 1 inch.

1.5 in. The hexagonal weights are identical. What is the surface

area of the barbell?

2 in.

3.5 in.

REASONING Find the surface area of the solid. Round your answer to the nearest tenth.

15. 4 in. 2 in. 16. 1 ft 4 ft 17. 7 mm

5 ft

10 in. 24 mm

25 mm

4 ft

10 mm

8 ft

18. The cube is made with 27 identical cubes. All cubes that

cannot be seen are orange. Is the surface area of the solid formed

without the purple cubes greater than, less than, or equal to the

surface area of the solid formed without the green cubes? Explain

your reasoning.

Find the area. SKILLS REVIEW HANDBOOK

19. 20. 21. 7 in.

2 ft 4 cm 5 in.

8 cm 12 in.

5 ft

22. MULTIPLE CHOICE A cliff swallow nest is 86 meters above a canyon floor.

The elevation of the nest is −56 meters. What is the elevation of the canyon

floor? SECTION 2.4

A −142

○ B −30

○ ○

C 30 ○

D 142

Section 6.6 Surface Areas of Composite Solids 287

13. BATTERIES What is the percent increase in the surface area of the AAA battery

to the AA battery? Round your answer to the nearest tenth of a percent.

AAA battery AA battery

0.8 mm 1 mm

43 mm

3.8 mm 49 mm 5.5 mm

10 mm

14 mm

1.75 in. 5 in. 14. BARBELL The diameter of the handle of a barbell is 1 inch.

1.5 in. The hexagonal weights are identical. What is the surface

area of the barbell?

2 in.

3.5 in.

REASONING Find the surface area of the solid. Round your answer to the nearest tenth.

15. 4 in. 2 in. 16. 1 ft 4 ft 17. 7 mm

5 ft

10 in. 24 mm

25 mm

4 ft

10 mm

8 ft

18. The cube is made with 27 identical cubes. All cubes that

cannot be seen are orange. Is the surface area of the solid formed

without the purple cubes greater than, less than, or equal to the

surface area of the solid formed without the green cubes? Explain

your reasoning.

Find the area. SKILLS REVIEW HANDBOOK

19. 20. 21. 7 in.

2 ft 4 cm 5 in.

8 cm 12 in.

5 ft

22. MULTIPLE CHOICE A cliff swallow nest is 86 meters above a canyon floor.

The elevation of the nest is −56 meters. What is the elevation of the canyon

floor? SECTION 2.4

A −142

○ B −30

○ ○

C 30 ○

D 142

Section 6.6 Surface Areas of Composite Solids 287