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