Chapter 11 – Surface Area and Volume Answer Key

11.1 Polyhedrons

Answers

1. V = 8

2. F = 9

3. E = 30

4. F = 6

5. E = 6

6. V = 6

7. F = 9

8. V = 6

9. Hexagonal pyramid. F = 7, V = 7, E = 12

10. No, a cone has a curved face.

11. Hexagonal prism. F = 8, V = 12, E = 18

12. No, a hemisphere has a curved face.

13. Trapezoidal prism. F = 6, V = 8, E = 12

14. The truncated icosahedron has 60 vertices, by Euler’s Theorem.

15. Regular dodecahedron, 1/3

16. 19

17. 1 red face, 8 yellow faces, 7 blue faces and 4 green faces

CK­12 Geometry Concepts 1

Chapter 11 – Surface Area and Volume Answer Key

11.2 Cross­Sections and Nets

Answers

1. Rectangle

2. Trapezoid

3. 4. 5.

6. 7.

8. Regular Icosahedron

9. Decagonal Pyramid

10. Trapezoidal Prism

11. Cube

12. All 11 nets

CK­12 Geometry Concepts 2

Chapter 11 – Surface Area and Volume Answer Key

CK­12 Geometry Concepts 3

Chapter 11 – Surface Area and Volume Answer Key

13. Regular Tetrahedron

14. Use the construction directions from #13 to make an equilateral triangle with midsegments. Using one of the midpoints of the equilateral triangle as a vertex, construct another

adjacent equilateral triangle with midsegments. Your result should look like the picture below.

15. No

CK­12 Geometry Concepts 4

Chapter 11 – Surface Area and Volume Answer Key

11.3 Prisms

Answers

1. Right Triangles, 6 u 2 each

2. 3x6, 4x6, 5x6; 18 u 2 , 24 u 2 , 30 u 2

3. 72 u 2

4. 84 u 2

5. 36 u 3

6. Lateral surface area is the area of all the sides, total surface area includes the bases.

7. a) 96 in 2

b) 192 in 2

c) 128 in 3

8. 1607.37 u 2 , 3960 u 3

9. 830.02 u 2 , 902.54 u 3

10. 182 u 2 , 147 u 3

11. x = 8

12. x = 25

13. 4060 ft 2

14. 2940 ft 2

15. 5320 ft 2

16. 495,000 ft. 3

17. x 2 – 16 in 2 , x = 25 in

18. 960; yes

19. 280 in 3

20. 6 in

CK­12 Geometry Concepts 5

Chapter 11 – Surface Area and Volume Answer Key

CK­12 Geometry Concepts 6

Chapter 11 – Surface Area and Volume Answer Key

11.4 Cylinders

Answers

1. rectangle, 2π rh

2. 350π cm 2

3. 486π u 2 , 1458π u 3

4. 34π u 2 , 16π u 3

5. x = 40

6. 60π in 2

7. 4100π cm 2

8. The height could be 1, 3, 5, or 15.

9. 5 in by 4 + 1 in, 20 + 5 in 2 67.83 in 2π π ≈

10. , x = 8x π25 2

11. No, explanations will vary.

12. 4π in 3

13. r = 9

14. 294π in 3

15. 24000π cm 3

16. 75π m 3

CK­12 Geometry Concepts 7

Chapter 11 – Surface Area and Volume Answer Key

11.5 Pyramids

Answers

1. vertex

2. y

3. lateral edge

4. w

5. z

6. t

7. 671 u 2 , 9680 u 3

8. 136 u 2 , 1280 u 3

9. 360 u 2 , 400 u 3

10. 896 u 2 , 1568 u 3

11. 36 √3 12. s2√3 13. 10 in

14. 13 in

15. 360 in 2

16. 9√3 17. 2√6 18. 8 1 √2 19. s 1

123√2

20. Find the volume of one square pyramid then multiply it by 2.

21. 2 7 √3 22. s 3

1 3√2

CK­12 Geometry Concepts 8

Chapter 11 – Surface Area and Volume Answer Key

CK­12 Geometry Concepts 9

Chapter 11 – Surface Area and Volume Answer Key

11.6 Cones

Answers

1. 450 u 2 , 1080 u 3

2. 1669 u 2 , 1680 u 3

3. 480 u 2 , 600 u 3

4. 576; 321.53

5. 1159.25

6. 1152.23

7. 1473.76

8. 100.8 °

9. 7

10. 24

11. 175 π

12. 32 u 3

13. 12 u 3

14. 60 u 3

15. h = 3.6 cm

16. r = 3 cm

17. 15 ft

CK­12 Geometry Concepts 10

Chapter 11 – Surface Area and Volume Answer Key

11.7 Spheres

Answers

1. No, all the cross sections must be circles because there are no edges.

2. SA = 256π in 2

V = π in 332048

3. SA = 324π cm 2

V = 972π cm 3

4. SA = 1600π ft 2

V = π ft 3332000

5. SA = 16π m 2

V = π m 2332

6. SA = 900π ft 2

V = 4500π ft 3

7. SA = 1024π in 2

V = π in 3316384

8. SA = 676π cm 2

V = π cm 338788

9. SA = 2500π yd 2

V = π yd 3362500

10. r = 5.5 in

11. r = 33 m

12. V = π ft 334

13. SA = 36π mi 2

14. r = 4.31 cm

CK­12 Geometry Concepts 11

Chapter 11 – Surface Area and Volume Answer Key

15. r = 7.5 ft.

16. a) 24429 in 3

b) 732.87 lbs

c) 50 in

17. 25,132.74 mi

18. 201 million mi 2

19. 268 billion mi 3

CK­12 Geometry Concepts 12

Chapter 11 – Surface Area and Volume Answer Key

11.8 Composite Solids

Answers

1. 36891.56 cm 3

2. 15901.92 cm 3

3. 300.44 in 3

4. 1900π u 2 , π u 3

5. 4680 ft 2 , 41,067π u 3

6. 91.875π units 2 , 104.125π u 3

7. cm, SA = cm 2h = 320

3350π

8. 14.14 in 3

9. 21.51in 3

10. 12 in 3π

11. 19 minutes

12. a) SA = 2 r 2 + 2 rhπ π

b) SA = 4 r 2π

c) SA = 4 r 2π

d) Answers will vary

13. 112 in 3

14. 190.87 cm 3

15. 471.24 cm 3

CK­12 Geometry Concepts 13

Chapter 11 – Surface Area and Volume Answer Key

11.9 Area and Volume of Similar Solids

Answers

1. No, ≠1014

3542

2. Yes, the scale factor is 4:3.

3. Yes, the scale factor is 3:5.

4. No, the top base is not in the same proportion as the rest of the given lengths.

5. Yes, cubes have the same length for each side. So, comparing two cubes, the scale factor is just the ratio of the sides.

6. 1:16

7. 8:343

8. 125:729

9. 8:11

10. 5:12

11. 87.48π

12. The volume would be 4 3 or 64 times larger.

13. 4:9

14. 60 cm

15. 91125 m 3

16. 2:3

17. 4:9

18. y = 8, x = h = 12

19. , z w = 4√5 = 6√5 20. 70.67, V 76V s = 1 l = 5

21. 6 , LA 6 LAs = 1 √5 l = 3 √5 22. 9:25, about 2.78 times as strong

23. 27:125

CK­12 Geometry Concepts 14