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Course 1 • Chapter 10 Volume and Surface Area 145

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Lesson 1 Homework PracticeVolume of Rectangular Prisms

Find the volume of each prism.

1.

7 yd

5 yd

9 yd

2. 10 mm 6 mm

3 mm

3. 4 in.9 in.13

6 in.12

4.

12 ft

3 ft6 ft

5.

4 m

4 m

13 m

6.

8 yd

2 yd12

5 yd34

7. MUSIC Find the volume of the CD box shown at the right.

8. TOYS Geneva’s younger brother has a toy box that is 3.6 feet long, 2.4 feet wide, and 1.5 feet high. What is the volume of the toy box?

9. What is the volume of a rectangular prism with a length of 11 meters, width of 26 meters, and height of 38 meters?

10. BAKING The bread loaf pan shown is filled to a height of 2 inches with banana bread batter. How much more batter could the pan hold before it overflowed?

6.25 in.

7.5 in.

8 in.

9 in.5 in.

3 in.

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146 Course 1 • Chapter 10 Volume and Surface Area

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use.Lesson 1 Skills PracticeVolume of Rectangular Prisms

Find the volume of each prism.

1. 2 in.

1 in.4 in.

2.

4 m

2 m7 m

3.

9 ft

6 ft5 ft

4.

4 mm

1 mm

10 mm

5.

3 in.2 in.

10 in.

6.

12 yd

10 yd

15 yd

7.

2 in.

3 in.5 in.

8. 2 ft5 ft

20 ft

9.

10 mm

7 mm

6 mm

Find the missing dimension of each prism.

10.

8.4 m

ℓ1 m

V = 39.48 m3 11.

h

7 ft12

14

3 ft34

V = 56 ft3 12.

7 yd

w

9 yd

V = 189 yd3

13. Find the volume of a rectangular prism with length 9 meters, width 4 meters, and height 5 meters.

14. What is the volume of a rectangular prism with length 6 yards, width 3 yards, and a height of 2 yards?

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use.Lesson 1 Problem-Solving PracticeVolume of Rectangular Prisms

1. OLYMPICS Olympic gold medal winner Michael Phelps competes in a pool with required dimensions 25 meters by 50 meters by 2 meters. What is the volume of the Olympic-sized pool? Explain how you found youranswer.

2. DUMP TRUCKS Raphael drives a standard-sized dump truck. The dimensions of the bed of the truck are length 15 feet, width 8 feet, and height 6 feet. What is the volume of the bed of the dump truck?

3. GIFTS William has some antique bottles. He is going to fill the bottles with bath soap and give them away as gifts. Use the figure to find the volume up to the fill line of abottle.

6 in.

3 in.4 in.

Fill Line

4. JEWELRY Janine keeps her jewelry in a jewelry box like the figure below. Find the volume of Janine’s jewelry box.

5 in.3 in.5

8

9 in.14

5. RECYCLING The town of Riverview provides a rectangular recycling bin for newspapers to each household. If the volume is 3,840 cubic inches, what is the height of the recycling bin?

h in.

12 in.

20 in.

6. CANDLE MAKING Kyle fills the candle mold with liquid candle wax. If the candle has a volume of 99 cubic inches, what is the width of themold?

3 in.w in.

11 in.

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Find the volume of each prism. Round to the nearest tenth if necessary.

1.

11 yd

14 yd9.5 yd

2.

8 m

12 m

9 m

3.

11.7 ft

10 ft

10 ft6 ft

4.

18 km

21 km

20 km

5. 1.7 in.

0.9 in.

1.7 in.1.7 in.

1.5 in.

6.

4 m 7 m

10 m

10.8 m

7. 5 in.

2.2 in.

3 in.

3.2 in. 3.2 in.

8.

6 cm

15 cm

10 cm

9.

6 cm

8 cm

4 cm

7.2 cm

10. WEDGE The base of a triangular door wedge has an area of 55 square centimeters. The height of the wedge is 5 centimeters. Find the volume of the door wedge.

11. GAME A wooden peg game in the shape of a triangular prism is 2 inches tall. The triangle has a base of 12 inches and a height of 9 inches. Find the volume of the game.

Lesson 2 Homework PracticeVolume of Triangular Prisms


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use.Lesson 2 Skills PracticeVolume of Triangular Prisms

Find the volume of each prism. Round to the nearest tenth if necessary.

1.

8 yd5 yd1

2

7 yd34

2.

4.8 m5.9 m

6.1 m

3. 4.2 ft2 ft

3.5 ft

4.

6 m

8 m

12 m

5.

2.6 m5.1 m

4.1 m

6. 15.2 in.

10.4 in.

18.4 in.

9.6 in.

7.

12 ft

15 ft7 ft

8.

5.7 cm

8.9 cm

13.7 cm

9.

6 m6 m

10.5 m

5.3 m

6 m


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use.Lesson 2 Problem-Solving PracticeVolume of Triangular Prisms

1. TOY BLOCKS A set of wooden blocks includes a triangular prism like the one shown below. Find the volume of the block.

3.5 cm

4 cm

2 cm

2. RAMP The base of a bicycle ramp has an area of 4 square feet. The ramp is a triangular prism. If the ramp has a

height of 2 1 − 2 feet, what is the volume of

the ramp?

3. CLAY A potter crafts a triangular prism out of clay. The height of the clay prism is 9 centimeters. Each triangle has a base of 12 centimeters and a height of 4 centimeters. What is the volume of the clay piece?

4. CABIN An A-frame cabin is built in the shape of a triangular prism, as shown. The front wall of the cabin has a length of 9 meters and a height of 7 meters. The cabin is 13 meters deep. Find the volume of the cabin.

7 m

9 m

13 m

5. PAPERWEIGHT A novelty paperweight has a triangular base with an area of 15 square centimeters. If the height of the paperweight is 1.5 centimeters, what is the volume of the paperweight?

6. SANDBOX Mr. Riojas is building his children a sandbox that is shaped like a triangular prism. He uses 7-foot-long wooden beams for each side of the base. He measures the height of the triangular base to be 6.1 feet. If he makes the sandbox 1 foot tall, how much sand will he need to fill it? Round to the nearest cubic foot.


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Lesson 3 Homework PracticeSurface Area of Rectangular Prisms

Find the surface area of each rectangular prism.

1.

3 yd5 yd

9 yd

2.

4 m

7 m

8 m

3.

3.8 cm

3.8 cm12 cm

4.

3 in.9 in.1

2

1 in.12

5.

20 ft26 ft

32 ft

6.

17 mm5 mm

4 mm

7. GIFTS Minh is covering a necklace box with gift wrap. The necklace box is 15 centimeters long, 8 centimeters wide, and 2 centimeters high. What is the minimum surface area of the paper that will cover the necklace box?

8. ESTIMATION Alicia estimates that the surface area of a rectangular prism with a length of 11 meters, a width of 5.6 meters, and a height of 7.2 meters is about 334 cubic meters. Is her estimate reasonable? Explain your reasoning.

9. BLOCKS Find the surface area of each

3 in. 2 in. 6 in.5 in.4 in. 5 in.

block. Which block has the greater surface area? Does the same block have a greater volume? Explain.


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use.Lesson 3 Skills PracticeSurface Area of Rectangular Prisms

Find the surface area of each rectangular prism.

1.

1 cm

2 cm

5 cm

2.

8 ft

4 ft3 ft

3.

7 in.

9 in.

4 in.

4.

2 yd

4 yd2 yd

5.

7 ft

5 ft3 ft

6. 2 ft

4 ft9 ft

7.

2 m

9 m

4 m

8. 3 in.

6 in.12

7 in.14

9.

4.3 mm

4.3 mm4.3 mm

10. Find the surface area of a rectangular prism that is 3 feet by 4 feetby 6 feet.

11. What is the surface area of a rectangular prism that measures 12 metersby 11 meters by 9 meters?


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use.Lesson 3 Problem-Solving PracticeSurface Area of Rectangular Prisms

1. GIFTS Fatima is wrapping a gift box for her nephew’s birthday. The box’s dimensions are 16 inches long by 10 inches wide by 5 inches high. What is the surface area of the box?

2. FOOD Antoine is wrapping a block of cheese that is 22 centimeters long by 6 centimeters high by 10 centimeters wide with plastic wrap. What is the surface area of the cheese block?

3. PAINTING Cody is painting the front door of his house. The dimensions of the door are 80 inches by 36 inches by 2 inches. If he paints all of the surfaces, how much area will he paint? Explain.

4. CARPENTRY Bryan is sanding a set of speaker boxes that he built for his room. What is the surface area of each box?

4.6 ft

2.2 ft1.1 ft

5. CARPENTRY Jing is putting oak veneer (thin wood covering) on the entire surface of her hope chest. How much veneer will she need?

5 ft14

2 ft14

3 ft12

6. TOY MAKING Trey is covering blocks of wood with wallpaper to make building blocks for his little sister. If he covers all the surfaces, how much wallpaper will he need? Think of a short way to solve this problem and explain.

3 in.

3 in.

3 in.


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Lesson 4 Homework PracticeSurface Area of Triangular Prisms

Find the surface area of each triangular prism. Round to the nearest tenthif necessary.

1.

6 km 14 km

6 km

6 km5.2 km

2.

2.6 ft

6.5 ft

3 ft

4 ft

3.

17 in.

12 in.

23.2 in.

24 in.

16.4 in. 4.

6.5 mm

2.5 mm8 mm

6 mm

5. One foam block on the playground at Teeny Tots Preschool isa triangular prism. About how much material is used to coverthe block? 6 in.

12 in.

13.4 in.

15 in.

6. The box for the jungle animal figurines is in the shape of a triangular prism. What is the surface area of the box?

7. The storage box for a flag is in the shape of a triangular prism. What isthe surface area of the box?

5 in.

5 in.4.3 in.

5 in.

12 in.

12 in.17.1 in.

4 in.24.5 in.


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use.Lesson 4 Skills PracticeSurface Area of Triangular Prisms

Find the surface area of each triangular prism. Round to the nearest tenth if necessary.

1.

15 yd

20 yd

25 yd

10 yd

2.

24 km18 km

25 km

7 km

3.

14 ft

10.5 ft

17.4 ft

11.9 ft

7 ft 4.

15.6 m

10.4 m 13 m15.6 m

13 m

5.

12.75 in.1.25 in.

5 in.

3 in.

9.25 in. 6.

36 mm

33 mm

46.8 mm

30 mm

7. A box of snack crackers is in the shape of a triangular prism. What is the surface area of the box?

5 cm4.3 cm

5 cm14 cm

5 cm


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use.Lesson 4 Problem-Solving PracticeSurface Area of Triangular Prisms

1. PIZZA Find the amount of cardboard needed to make a box for a single slice of pizza. The box is in the shape of a triangular prism as shown.

12.5 in.

12 in.

2 in.

7 in.

2. RAMPS Sturdy Steel Construction is building a steel ramp in the shape of a triangular prism. The dimensions are shown below. What is the surface area of the ramp?

12 ft

13 ft

84 ft

85 ft

3. CAMPING The Canvas Camping Company makes canvas tents like the one shown. How much material is needed to make the tent?

3 ft 3 ft

6 ft5.1 ft

6 ft9 ft

4. DISPLAY CASES Find the surface area of Anna’s glass doll display case. The case is in the shape of a triangular prism as shown.

7 in.

15 in.

10 in.

10 in.14

10 in.14

5. GIFTS Mariska purchased a gift box in the shape of a triangular prism. The dimensions are shown below. What is the surface area of the gift box?

35 cm

42 cm30 cm

18 cm

6. PACKAGING Pascal’s Peanut Company packages dry-roasted peanuts in a box in the shape of a triangular prism. The dimensions are shown below. What is the surface area of the box?

20.8 cm13 cm

7.8 cm

13 cm

18.2 cm


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Lesson 5 Homework PracticeSurface Area of Pyramids

Find the surface area of each pyramid.

1.

9 km

16 km

9 km

2.

4 ft4 ft

5 ft 3.

1 yd14

2 yd

1 yd14

4.

8 in.

8 in.

6.9 in.

8 in.

5.

5.2 mm

6 mm6 mm

6 mm8.9 mm

6.

4.3 m5 m5 m

5 m7 m

7. GOLF Marshall purchased a pyramid-shapedgolf ball display case with the dimensionsshown. What is the surface area of the case?Round to the nearest hundredth.

8. PUZZLES Potter’s Puzzles sells a wooden pyramid puzzle. The base is a square with side lengths of 6 inches. The slant height is 10 inches. What is the surface area of the puzzle?

9. ART Mariah is painting the surface ofa sculpture in the shape of a square pyramid. The base has side lengths of 32 centimeters. The slant height is 25 centimeters. What is the surface area of the sculpture?

GOLF

4.78 in.5.25 in.

5.25 in.5.25 in.

4.55 in.


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use.Lesson 5 Skills PracticeSurface Area of Pyramids

Find the surface area of each pyramid. Round to the nearest tenth if necessary.

1.

7.3 m

4 m4 m

2.

12.7 ft

5 ft5 ft

3.

11.5 yd

7 yd7 yd

4.

11 cm11 cm

6.6 cm

11 cm9 cm 5.

9 in. 9 in.

7.8 in.9 in.

7.8 in.

6. 15 mm

12 mm

12 mm

10.2 mm

12 mm

7.

26 cm

8 cm

26 cm

8. 8.7 ft

10 ft 10 ft

10 ft

8.7 ft

9.

12 yd10 yd

10 yd

7 yd10 yd

10. OFFICE DÉCOR Mr. Statsko has a paper weighton his desk in the shape of a square pyramid. Thedimensions of the pyramid are shown. What is thesurface area of the paper weight?

4 in.

6 in.6 in.


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use.Lesson 5 Problem-Solving PracticeSurface Area of Pyramids

1. FOUNTAINS A sculpture in the water fountain at Casey Creek Park is in the shape of a square pyramid. The base of the sculpture is 2 feet long and 2 feet wide. The slant height is 5 feet. What is the surface area of the sculpture?

2. TENTS Tent Potential, Inc. makes a tent in the shape of a square pyramid. The base of the tent is 3.4 meters long and 3.4 meters wide. The slant height of the tent is 2 meters. What is the surface area of the tent?

3. STAGE SET Rock It Out builds stage sets for rock concerts in the shape of a square pyramid. One set has a base that is 12 feet long and 12 feet wide. The slant height of the set is 13.4 feet. What is the surface area of the stage set?

4. TOYS Toddler Builders makes a toy block in the shape of a triangular pyramid. The base of the block is an equilateral triangle with dimensionsof 6 inches. The height of the base is5.2 inches and the slant height of the block is 8 inches. What is the surface area of the pyramid block?

5. PARACHUTES Marcus’s science class is testing a toy parachute in the shape of a square pyramid. The opening at the base is 20 centimeters long and 20 centimeters wide. The slant height of the parachute is 14.1 centimeters. What is the surface area of the parachute? (Hint: The surface area of the parachute does not include the base.)

6. ARCHITECTURE Glass skylights on the roof of Jezebelle’s apartment building are in the shape of a square pyramid. The base of each skylight is 8 feet long and 8 feet wide. The slant height is6.4 feet. How much glass is used to make each skylight? (Hint: The skylight does not have a glass base.)

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