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452GeometryChapter 12 Resource Book

LESSON

12.7 Practice BFor use with pages 880–888

Tell whether the pair of right solids is similar. If so, determine the scale factor.

1.

14 cm6 cm

7 cm

4 cm

3 cm

8 cm

2. 3 ft

2 ft

6 ft

4 ft

3.

10 mm6 mm

4 mm 4 mm

4 mm5 mm

4.

3 m

2 m

1.8 m2.7 m

1.2 m

4.5 m

5. Multiple Choice Which set of dimensions corresponds 5 in.

9 in.

to a right cylinder that is similar to the cylinder shown?

A. r 5 2, h 5 5 B. r 5 3, h 5 7

C. r 5 10, h 5 19 D. r 5 15, h 5 27

Solid A (shown) is similar to Solid B (not shown) with the given scale factor of A to B. Find the surface area and volume of Solid B.

6. Scale factor of 1: 2 7. Scale factor of 1: 3 8. Scale factor of 2: 3

A

S 5 42 ft2, V 5 36 ft3p p

A

S 5 96 m2, V 5 96 m3p p

A

S 5 75.6 cm2, V 5 36 cm3

9. Finding Surface Area Two spheres have a scale factor of 1 : 3. The smaller sphere has a surface area of 16π square feet. Find the surface area of the larger sphere.

10. Multiple Choice Two right cylinders are similar. The surface areas are 24π and 96π. What is the ratio of the volumes of the cylinders?

A. 1 }

4 B.

1 }

8 C.

1 }

2 D.

2 }

3

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453Geometry

Chapter 12 Resource Book

Solid A is similar to Solid B. Find the scale factor of Solid A to Solid B.

11.

S = 208 m2 S = 52 m2

AB

12.

BA

S = 63p cm2 S = 28p cm2

13.

V = 27 ft3

V = 64 ft3

A

B

14.

A

B

V = 54 in.3 V = 16 in.3

Solid A is similar to Solid B. Find the surface area and volume of Solid B.

15.

3 m2

4 m4 m

8 m

4 mA

B

16. 18 mm

12 mm 10 mmA B

17. Finding a Ratio Two cubes have volumes of 64 cubic feet and 216 cubic feet. What is the ratio of the surface area of the smaller cube to the surface area of the larger cube?

In Exercises 18–22, use the following information.

Water Tower As part of a class project, you obtain the responsibility 12 ft

16 ft

of making a scale model of the water tower in your town. The water tower’s diameter is 12 feet and the height is 16 feet. You decide that 0.5 inch in your model will correspond to 12 inches of the actual water tower.

18. What is the scale factor?

19. What is the radius and height of the model?

20. What is the surface area of the model?

21. What is the volume of the actual water tower? of the model?

22. Suppose you make a second scale model congruent to the fi rst. What is the ratio of their surface areas? of their volumes?

LESSON

12.7 Practice B continuedFor use with pages 880–888

LES

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A63Geometry

Chapter 12 Resource Book

20. 4 in.; 64π in.2; 256

} 3 π in.3

21. 7 }

2 ft; 7π ft;

343 }

6 π ft3

22. 6 m; 12π m; 144π m2 23. 18 cm

24. 8.87 in.2 25. 2.48 in.3 26. 9.04 in.3

Practice Level C

1. 172.03 m2 2. 2.01 mi2 3. 79,422.6 mm2

4. 415.48 cm2 5. 226.19 in.2 6. 62.83 ft2

7. 2.1 m 8. 9.75 cm 9. 0.6 ft 10. 80π cm2

11. 2352.07 cm3 12. 606.13 ft3

13. 124,185.41 in.3 14. 10.31 m3 15. 21.77 mm3

16. 219.42 yd3 17. S 5 104.72 m2, V 5 77.57 m3

18. S 5 1009.61 ft2, V 5 2322.09 ft3

19. S 5 6597.34 cm2, V 5 38,788.74 cm3

20. π cm2 21. 16π in.2 22. 16π m2

23. 58.43 ft, 1086.87 ft2, 3369.28 ft3

24. 13.45 m, 2273.29 m2, 10,191.91 m3

25. 29 yd, 182.21 yd, 102,160.4 yd3

26. 11 cm, 69.12 cm, 1520.53 cm2

27. S ø 27,646 ft2, V ø 385,368.7 ft3; Surface Area 5 Surface area of cylinder 2 Area of one base 1 Surface Area of hemisphere; Volume 5 Volume of cylinder 1 Volume of hemisphere

28. about 52 cm3

Review for Mastery

1. 7853.98 ft2 2. 3 m 3. 78.54 ft2

4. 1436.76 yd3

Challenge Practice

1. s }

r 5

3 Ï}

4 π 2. rc

} rs

5 Î}

8 }

h 5

2 Ï}

2 }

Ï}

h

3. a. V 5 16

} 3 πr3 b. r > 0

c. Radius: 1.9 ft; length: 7.6 ft

4. (x 2 x0)2 1 (y 2 y0)2 1 (z 2 z0)2 5 r2

5. (x 1 4)2 1 (y 2 3)2 1 (z 2 5)2 5 81

6. 1 x 2 5 } 2 2

2 1 (y 2 1)2 1 z2 5

97 } 4

7. V 5 4 }

3 πabc 8. 1120π < 3518.6 cm3

Lesson 12.7Practice Level A

1. not similar 2. yes; 3 : 2 3. yes; 7 : 4

4. yes; 3 : 2 5. 3 : 1 6. 3 : 1 7. 3 : 1 8. 9 : 1

9. 27 : 1 10. D 11. S 5 832 m2, V 5 1536 m3

12. S 5 2464 ft2, V 5 4096 ft3

13. S 5 202.5π cm2, V 5 337.5π cm3 14. 1 : 2

15. 7 : 2 16. 5 : 6 17. 1 : 4 18. true 19. false

20. false 21. false 22. 4 : 1 23. 3750π yd3

24. 13,536 in.2

Practice Level B

1. similar; 2 : 1 2. similar; 3 : 2 3. not similar

4. similar; 1 : 0.6 5. D 6. 168π ft2; 288π ft3

7. 864π m2; 2592π m3 8. 170.1 cm2; 121.5 cm3 9. 144π ft2 10. B 11. 2 : 1

12. 2 : 3 13. 3 : 4 14. 3 : 2 15. about 385.6 m2; about 330.98 m3 16. 975π mm2; 4500π mm3

17. 4 : 9 18. 1 : 24 19. r 5 3 in.; h 5 8 in.

20. 66π in.2 21. 576π ft3; 72π in.3

22. 1:1; 1:1

Practice Level C

1. yes; 1 : 2 2. yes; 1 : 4 3. not similar

4. yes; 5 : 3 5. 256 in.2; 224 in.3

6. 2432π in.2, 15,360π in.3 7. 324 cm3; 1 : 3

8. 243 ft2; 182.25 ft3 9. S 5 90 cm2, V 5 50 cm3; S 5 810 cm2, V 5 1350 cm3 10. S ø 141.4 in.2, V ø 109.5 in.3; S ø 2262.4 in.2, V ø 7008 in.3

11. S ø 201.1 ft2, V ø 268.1 ft3; S ø 2463.0 ft2, V ø 11,494.0 ft3 12. 6: 5 13. 3 : 22 14. 450

15. 686 16. 7 17. 3, 5 18. 728π m2

19. 1920 yd3 20. smaller cylinder: r 5 4 cm, h 5 8 cm; larger cylinder: r 5 5 cm, h 5 10 cm;

21. 5.8 ft high, 5.5 ft wide, 12.8 ft long

22. 1.56 ft3 23. 1:1

Review for Mastery

1. Not similar; radius 3 }

9 5

1 } 3 , height

9 }

18 5

1 } 2

2. Similar; The scale factor is 5 : 8. 3. 1 : 2; Edge length of C is Ï

}

6 units; 48 Ï}

6 cubic units

Problem Solving Workshop:Mixed Problem Solving

1. a. 10,800 in.3 b. 72 in.3 c. 150

2. a. 576 in.2 b. 2250 in.3 c. 250

3. Answers will vary. 4. a. 48.11 in.3 b. yes; The juice has a volume of about 36.1 in.3, which is smaller than the volume of the cup.

Lesson 12.6, continuedA

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WE

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