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Answers
Geometry Copyright © Big Ideas Learning, LLC Answers All rights reserved. A108
27. 8 and 7x x= − = 28. 4 and 7x x= − =
29. 43x = 30. 102x = 31. 112x =
32. 18x = 33. 26x = 34. 84x =
35. 133x = 36. 26x = 37. 19x =
38. 1275x = 39. 34 40. 25
41. 82 42. 34 43. 8
44. 12 45. 9 46. 6
47. 18
48. a. 2 11x +
b. 6
c. 11
d. 17
49. ( )3, 3− − 50. 112,
2 −
51. 11,
2 − −
52. 15 7,
2 2 −
53. 13 7,
2 2 − −
54. 11, 6
2 −
55. 5 9,
2 2 −
56. 5 1,
2 2 − −
57. 745
58. 2 29 59. 233 60. 2 145
61. 365 62. 109 63. 569
64. 8
65. Sample answer: , , andABC ABD CBD∠ ∠ ∠
66. Sample answer: , , andGFJ GFH JFH∠ ∠ ∠
67. 107° 68. 113° 69. 2 130
70. 218 71. 3 65 72. 466
73. 8 2 74. 2 102
75. a. 18.4 in.
b. 44.4 in.
76. a. 7.6 in.
b. 17.6 in.
Chapter 11 11.1 Start Thinking
10 31.4 cmπ ≈
1. 5 15.7 cmπ ≈ 2. 57.9 cm
2
π ≈
3. 25
13.1 cm6
π ≈
11.1 Warm Up
1. 120 , 8π° 2. 90 ,15π° 3. 135 ,16π°
11.1 Cumulative Review Warm Up
1. 130° 2. 54
3. 164 2 41=
11.1 Practice A
1. 21 m 2. about 169.6 ft
3. about 47.1 in. 4. 12.4 cm
5. Divide the circumference of the tree by π to find the diameter of the tree. Because the diameter is 50 15.9 inches,π÷ ≈ which is less than 18 inches, the tree is not suitable for tapping.
6. about 6.28 cm 7. about 47.1 in.
8. about 7.33 ft 9. about 36.57 mm
10. about 86.85 in. 11. 3
π
12. 225° 13. 1257 ft
11.1 Practice B
1. 36
mπ
2. 10.8 ftπ
3. about 44.0 cm 4. 160°
5. 200° 6. about 19.54 m
7. about 24.43 m 8. 280°
9. about 34.21 m 10. about 114°
11. about 58.03 ft 12. about 20.53 cm
13. 7
12
π 14. 150°
15. a. 35.6 in. b. about 71 teeth
Answers
Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Answers
A109
11.1 Enrichment and Extension
1. a. 18 56.55 cmπ ≈ b. 6 18.85 cmπ ≈
2. 8 3. about 30.16 cm
4. about 36.85 cm 5. about 28.57 in
11.1 Puzzle Time
SO THAT THE AUDIENCE WOULD BE GLUED TO THEIR SEATS
11.2 Start Thinking 249 153.9 in.π ≈
1. 24977.0 in.
2
π ≈ 2. 2147115.5 in.
4
π ≈
3. 224542.8 in.
18
π ≈
11.2 Warm Up
1. 281 254.5 in.π ≈ 2. 24 12.6 ftπ ≈
3. 100
5.6 miπ
≈ 4. 42
2 7.3 mπ
≈
5. 236 113.1 cmπ ≈
11.2 Cumulative Review Warm Up
1. 4 3, 4x y= = 2. 7, 7 2x y= =
3. 22, 11x y= =
11.2 Practice A
1. 2145.27 ft 2. 2289.53 cm
3. 18 m 4. 30 in.
5. about 10,610 people/mi2
6. about 883,573 people
7. about 221.38 ft , about 2132.56 ft
8. about 2184.35 in. , about 2346.58 in.
9. about 21.22 m , about 21.92 m
10. about 225.13 cm , about 2175.93 cm
11. 2804.24 yd 12. about 212.57 m
13. about 285.13 ft 14. about 2879.65 mm
15. about 221.46 cm
16. coverage area is 4 times greater;
2
2
new coverage area 7260.57 ft4
old coverage area 1815.14 ft≈ ≈
11.2 Practice B
1. about 2143.14 in. 2. about 20.07 mi
3. about 4.5 km 4. about 36.4 yd
5. about 5.5 mi 6. about 10.5 mi
7. about 20.18 m , about 20.33 m
8. about 22.86 cm , about 223.56 cm
9. about 20.39 in. , about 20.84 in.
10. about 21.87 yd , about 26.86 yd
11. about 2.5 cm 12. about 0.6 ft
13. about 1099.56 m2 14. about 2230.91 ft
15. about 232.99 in. 16. about 326.18 in.
11.2 Enrichment and Extension
1. 3
π 2. 36°
3. 27m
3
π 4. 8 square unitsπ
5. a. 1
8 b.
3
8 c. 1
2
6. 236 3 62.4 cm≈
7. a.
b. 40
y xπ=
11.2 Puzzle Time
A SCREWDRIVER
Measure of arc, x
30° 60° 90° 120° 150° 180°
Area of sector, y
3
4
π
3
2
π
9
4
π 3π
15
4
π 9
2
π
Answers
Geometry Copyright © Big Ideas Learning, LLC Answers All rights reserved. A110
11.3 Start Thinking
1. Sample answer: To find the area of the triangle, draw an altitude and create two congruent 30 -60 -90° ° ° triangles. Using the special right triangle, the altitude would have a measure of
2 3 units. Using the formula for the area of a triangle, you have
( )( )1 14 2 3
2 2A bh= = = 4 3 square units.
2. Sample answer: To find the area of the regular hexagon, connect two pairs of non-consecutive vertices and create four congruent 30 -60 -90° ° ° triangles and a rectangle as shown. Using the special right triangle, you can find the measures needed to calculate the area. The area of the hexagon would be the sum of the areas of the four congruent triangles and the rectangle in the center, or
( )( ) ( )14 2 3 2 4 4 3
2
24 3 square units.
A = +
=
11.3 Warm Up
1. 4 5 8.9≈ 2. 15 sin 45 10.6° ≈
3. 4.6
5.4cos 32
š
11.3 Cumulative Review Warm Up
1. sometimes 2. always 3. always
4. never 5. always 6. sometimes
11.3 Practice A
1. 202.5 square units 2. 54 square units
3. 126 square units 4. 120 square units
5. 40° 6. 22.5° 7. 18°
8. 12.9° 9. 60° 10. 30°
11. 60° 12. 120°
13. 32.4 square units 14. 554.4 square units
15. 1119.6 square units 16. 178 cm2
17. 1175.6 m2
18. a. about 73.9 ft
b. 3 containers; The area of the floor is about 416.5 square feet. Because 416.5 200 2.08÷ ≈ and you cannot buy part of a container, you will need 3 containers of wood sealer.
11.3 Practice B
1. 285.25 square units 2. 110.36 square units
3. 252.5 square units 4. 384 square units
5. 51.4° 6. 25.7° 7. 64.3°
8. 154.3° 9. 27.5 square units
10. 8.7 square units 11. 3.9 square units
12. 16 ft, 48 ft 13. 22 mm, 44 mm
14. a. Sample answer:
b. 1481 ft2
15. yes; One side length of the 11-gon is 16.5
1.5 meters.11
= The length of the apothem a is
0.75.
tan 16.4a =
° So,
( )1 0.7516.5
2 tan 16.4A
= ≈ °
21 square meters.
11.3 Enrichment and Extension
1. 21.5 ft 2. 32
π+
3. 20
3
4A s= 4. 23
36s
5. 3; 2 21
3 3
4 12A s s= +
60°2
2 3 4120°
8 ft
15 ft
Answers
Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Answers
A111
6. 2 2 22
3 3 3
4 12 27A s s s= + +
7. 2 2 2 23
3 3 3 4 3
4 12 27 243A s s s s= + + +
8. 9
5S =
9. 22 3 square units
5nA s=
11.3 Puzzle Time
A WATCH DOG
11.4 Start Thinking
triangular prism: 5,F = 6,V = 9,E = rectangular prism: 6,F = 8,V = 12,E = pentagonal prism:
7,F = 10,V = 15,E = hexagonal prism: 8,F = 12,V = 18;E = 2F V E+ − = for each of the
prisms; As you increase the number of faces by 1, the numbers of vertices increases by 2, and the number of edges increases by 3.
11.4 Warm Up
1. yes
2. no; The sides are not segments.
3. no; It is not a plane figure.
11.4 Cumulative Review Warm Up
1. 8 2. 29 3. 313
6
11.4 Practice A
1. yes; rectangular prism 2. yes; triangular pyramid
3. no 4. circle
5. triangle 6. rectangle
7.
cylinder with height 9 and base radius 5
8.
sphere with radius 2
9.
cone with height 6 and base radius 4
10. yes; It is bounded by polygons only.
11.
yes; Sample answer: parallel to a horizontal face and parallel to a vertical face
12. a. 4 4 5 12.94 in.+ ≈
b. 24 5 8.94 in.≈
11.4 Practice B
1. triangle 2. trapezoid 3. semicircle
4.
cylinder with height 6 and base radius 6
5.
Sample answer: part of a cone with height 3 and two different circular bases with radii 2 and 4
9
5
2
2
4
6
6
6
2
43
Answers
Geometry Copyright © Big Ideas Learning, LLC Answers All rights reserved. A112
6.
hemisphere with radius 9
7. none of the parts are polyhedrons; Sample answer: Two parts contain some faces that are polygons, but all three parts also contain faces that are not polygons.
8.
Sample answer: two adjacent cylinders that share the same axis of symmetry
9. a. trapezoid, triangle
b. trapezoid: perimeter 12 2 13= + ≈ 19.21 in.,2area 18 in.=
triangle: perimeter 4 2 13 11.21 in.,= + ≈ 2area 6 in.=
c. no; Sample answer: It is flatter than a circle, more like an oval.
11.4 Enrichment and Extension
1.
2.
3. circle
4. no; Sample answer: An oblique cylinder does not have rotational symmetry, so you cannot draw a shape and an axis of revolution that could form the cylinder.
5. 6.
7.
11.4 Puzzle Time
BECAUSE THEY HAD JUST FINISHED A MARCH OF THIRTY-ONE DAYS
11.5 Start Thinking
964
π cubic units; 964
π cubic units; no; no; The volume
of a right solid and an oblique solid will be the same if the height and cross-sectional area are the same.
11.5 Warm Up
1. 3168 cm 2. 3480 in.
3. 330 94.2 cmπ ≈
11.5 Cumulative Review Warm Up
1. 0.6561 2. 0.9903 3. 0.2679−
4. 0.5299− 5. 0.9925− 6. 4.3315−
11.5 Practice A
1. 384 in. 2. 3864 cm
3. about 3314.16 ft 4. about 31130.97 yd
9
9
6
8
23
(0, 4, 0)
(0, 0, 5)
y
z
x
(−3, 0, 0)(0, 0, 2)
y
z
x
Answers
Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Answers
A113
5. about 2497 g 6. 6 m
7. about 11.00 in.
8. 212 ft ; Sample answer: length: 4 ft, width: 3 ft
9. 224 cm ; Sample answer: length: 4 cm, width 6 cm
10. 337.5 m3 11. 323 cm3
12. about 3383.87 gallons
11.5 Practice B
1. 3288 ft 2. 317.28 m
3. about 10,433.62 in.3 4. about 1334.55 cm3
5. 3700 g 6. 4 ft 7. about 3.00 m
8. 18 yd2; Sample answer: length: 6 yd, width: 3 yd
9. 32 in.2; Sample answer: length: 8 in., width: 4 in.
10. 3378 in.π 11. about 174 ft3 12. 144 in.3
11.5 Enrichment and Extension
1. 3 2 2V x x x= + −
2. 3 22V x x xπ π π= + +
3. 7 5
4. Sample answer: The volume is equal to the surface area, so 2 22 2 .r h r rhπ π π= + Solve for r to
obtain 2
. 2
hr
h=
− If 0 2,h< < then 0,r <
so h must be greater than 2. Similarly, if you solve
for h, you get 2
.2
rh
r=
− If 0 2,r< < then
0,h < so r must be greater than 2.
5. 31280 3 2217.0 cm≈
6. 3125 3 680.2 in.π ≈
7. 3736 2312.2 cmπ ≈
8. 5 in. 9. 5 ft
11.5 Puzzle Time
POST OFFICE
11.6 Start Thinking
Sample answer: The volume of the cube is clearly greater than the volume of the pyramid. You can see that the pyramid would fit inside the cube. The volume of the cube is 125 cubic inches and the volume of the pyramid will be one third of that value.
11.6 Warm Up
1. 2210 in. 2. 217.5 m
3. 245 tan 54 61.9 cm° ≈
11.6 Cumulative Review Warm Up
1. ( ) ( )2 22 5 49x y− + − =
2. ( ) ( )2 23 9 9x y+ + − =
3. ( ) ( )2 28 4 64x y− + + =
4. ( ) ( )2 211 3 169x y+ + + =
11.6 Practice A
1. 3240 m 2. 3845 in. 3. 384 ft
4. 8 cm 5. 7.5 ft 6. 12 m
7. 32 in.3 8. 1024 mm3 9. 704 yd3
10. 1155 m3 11. 960 cm3 12. 98 23 3
, or 32 m
11.6 Practice B
1. about 367.04 cm3 2. about 96.99 ft3
3. about 643.79 yd3 4. 6.3 m
5. 12.5 in. 6. 2211.84 cm3
7. 32.175 yd3 8. 290 cm3
9. 3840 in.3 10. 750 m3 11. 8
11.6 Enrichment and Extension
1. 96 cm3 2. 31000 2cm
3
3. 320 cubic units
4. Sample answer: ( )1 21
;3
V B h h= +
3433.3 unitsV ≈
Answers
Geometry Copyright © Big Ideas Learning, LLC Answers All rights reserved. A114
5. ( )3
10.91576 196 576 196
3
4029.43 cm
V = + + •
=
11.6 Puzzle Time
A CAR POOL
11.7 Start Thinking
5052.4 in.;
3π ≈
18 in.;
3 2250
261.8 in.3
π ≈
11.7 Warm Up
1. about 28.3 cm2 2. about 153.3 in.2
3. about 548.2 m2
11.7 Cumulative Review Warm Up
1. 2 8y x= − 2. 9y x= +
3. 1 14
5 5y x= −
11.7 Practice A
1. about 2377 ft 2. 537.2 m2
3. about 209.44 cm3 4. about 16.76 in.3
5. 35123
mmπ 6. 372
in.π
7. about 871.27 in.3 8. about 47.24 cm3
9. 3 ;h 3;r Sample answer: The original volume is 21
3V r hπ= and the new volume is 2 .V r hπ=
10. cylindrical container; The cost of the cylindrical container is $4.75 per 96π cubic inches (or about $0.02 per cubic inch), whereas the cost per cubic inch for the cone-shaped container is $3.25 per 32π cubic inches (or about $0.03 per cubic inch).
11.7 Practice B
1. about 593.8 yd2 2. about 379.3 mm2
3. about 1773.95 in.3 4. about 25.13 cm3
5. 37565
ftπ 6. 327449
mπ
7. about 2814.87 in.3 8. about 16.20 cm3
9. 1;
2h
2;
2r Sample answer: The original volume is
21
3V r hπ= and the new volume is 21
.6
V r hπ=
10. about 10.05 sec
11.7 Enrichment and Extension
1. a. 15 47.1 mπ ≈
b. 2225176.7 m
4π ≈
c. about 2389.6 m
2. 32ft
9
π 3. 32
ft3
π
4. 32 ftπ 5. about 3191.45 mπ
6. Sample answer: You are increasing the area of the base by a factor of 23 9,= so the height of the
cone must be 1
9 the original size.
7. 2282 885.9 ftπ ≈ 8. about 2634.3 m
11.7 Puzzle Time
BECAUSE THEY TAKE TOO LONG TO CHANGE
11.8 Start Thinking
( )2 2cube 6 9.55 547.2 in. ,S = ≈
( )2
cyl
2
9.55 9.552 9.55 2
2 2
429.8 in. ; no; cylinder
S π π = +
≈
11.8 Warm Up
1. 15 in. 2. 5 in. 3. 3 in.
11.8 Cumulative Review Warm Up
1. radius 2. tangent 3. diameter
4. chord 5. secant 6. radius
11.8 Practice A
1. about 50.27 in.2 2. about 314.16 mm2
3. about 201.06 ft2 4. 3 m
5. 9 yd 6. about 113.10 ft3
7. about 14,137.17 cm3 8. about 659.58 m3
Answers
Copyright © Big Ideas Learning, LLC Geometry All rights reserved. Answers
A115
9. about 4.19 in.3 10. about 9202.8 km3
11. about 3053.63 cm3 12. about 791.68 ft3
13. about 100.53 m2, about 134.04 m3
14. about 12.57 yd2; The edge length of the cube, 2 yards, is the diameter of the sphere.
15. surface area of new ball is 2 2
40 20
38 19 = =
2400
1.11361
≈
times the
surface area of the old ball (an 11% increase), volume of new ball is
3 340 20 8000
1.1738 19 6859 = = ≈
times the
volume of the old ball, (a 17% increase); Use the properties of similar solids;
surface area of new ball 1600 400,
surface area of old ball 1444 361
ππ
= =
volume of new ball 32,000 3 8000
volume of old ball 27,436 3 6859
ππ
= =
11.8 Practice B
1. about 113.10 m2 2. about 76.97 yd2
3. about 254.47 in.2 4. 5 cm
5. 2.5 in. 6. about 3053.63 ft3
7. about 575.17 cm3 8. about 4188.79 m3
9. 288 904.78π ≈ ft3 10. about 0.52 mi3
11. about 5089.38 yd3 12. about 83.78 in.3
13. surface area shrinks to one-fourth original size, volume shrinks to one-eight original size
14. a. no; You also need to know the radius of one of the cannonballs.
b. 9 lb
11.8 Enrichment and Extension
1. greater than; The volume of the box is 32 cubic inches. The volume of the four balls is less than 17 cubic inches. So, there is more than 15 cubic inches left over inside the box, and the volume of a fifth ball is less than 6 cubic inches, so the volume left over inside the box is greater than a fifth ball.
2. 1,876,578 L 3. 1.0 in.
4. a. 2
Sr
ππ
=
b. 6
S SV
ππ
=
c.
The shape of the graph is similar to half a parabola.
5.
6. 2 2 2 24 4 1S r r rπ π= + + +
7. 2 2 22 2S r r rπ π= + +
11.8 Puzzle Time
EGG SHELLS
Cumulative Review
1. 9 ft 2. 16 cm 3. 5 in.
4. 18 km 5. 11 m 6. 18 mm
7. ( )1, 2M 8. ( )1, 1M − 9. ( )3, 4M −
10. ( )8, 2M − 11. ( )3, 0H 12. ( )5, 3G −
13. ( )10, 5G − 14. ( )6, 8H − 15. 1
16. 386 17. 157 18. 74
19. 181 20. 6
21. , ,XYZ ZYX Y∠ ∠ ∠ 22. , ,JKL LKJ K∠ ∠ ∠
23. Sample answer: consecutive even integers beginning with 2; 12, 14
24. Sample answer: consecutive odd integers beginning with −1, alternatively negative and positive; 11, −13
S
V
4
6
8
2
4 6 82
V = S Sπ6π
r
r
r
πrπ
Answers
Geometry Copyright © Big Ideas Learning, LLC Answers All rights reserved. A116
25. Sample answer: skip two letters in the alphabet, beginning with A; P, S
26. Sample answer: skip one letter in the alphabet, beginning with B; L, N
27. 1x = − 28. 1x =
29. 6x = − 30. 1x =
31. 2x = 32. 3x =
33. 7x = − 34. 1x =
35. 4 7y x= − − 36. 5 2y x= +
37. 8y x= + 38. 10 6y x= − +
39. 35 50y x= − 40. 9 6y x= −
41. 3, 4x y= = 42. 15, 18x y= =
43. 15, 10x y= = 44. 21, 26x y= =
45. 54 46. 47
47. 26 48. 7
49. 3 39y x= − 50. 8 41y x= − −
51. 4 36y x= + 52. 2 1y x= − −
53. 13
4y x= − 54. 11y x= −
55. 27
3y x= − − 56. 8 26y x= − +
57. ( )9, 2A′ − 58. ( )6, 3B′ −
59. ( )6, 7C ′ − 60. ( )9,1D
61. ( )11, 3E − −
62. ( ) ( ) ( )10,11 , 6, 13 , 2, 9P Q R′ ′ ′− − −
63. ( ) ( ) ( )5, 4 , 9, 2 , 13, 6P Q R′ ′ ′− − −
64. ( ) ( ) ( )13, 1 , 9,1 , 5, 3P Q R′ ′ ′− − − − −
65. ( ) ( ) ( )1, 6 , 3, 4 , 7, 8P Q R′ ′ ′− − − −
66. ( ) ( ) ( )9, 1 , 5,1 , 1, 3P Q R′ ′ ′− − − − −
67. ( ) ( ) ( )27, 21 , 21, 0 , 0, 12A B C′ ′ ′− −
68. ( ) ( ) ( )4, 20 , 0, 22 , 22, 22X Y Z′ ′ ′− − −
69. ( ) ( ) ( )2, 0 , 4, 3 , 3, 2M N P′ ′ ′− −
70. ( ) ( ) ( ) ( )5, 4 , 0, 6 , 4, 5 , 3, 6Q R S T′ ′ ′ ′− − − −
71. ( ) ( ) ( ) ( )32, 8 , 32, 40 , 28, 16 , 24, 4D E F G′ ′ ′ ′−
72. a. 50.3 in.
b. 56 in.
c. 54 in.
73. a. 50.3 cm2
b. 49 cm2
c. 48 cm2
d. the circle
Chapter 12 12.1 Start Thinking
Sample answer:
1. Sample answer: It is not too likely that you will grab the number that matches your jersey. You have a 1 in 15 chance of choosing a matching pair of shorts.
2. Sample answer: Possible Outcomes: Jersey and shorts – 11 and 1, 11 and 2, 11 and 3, 11 and 4, 11 and 5, 11 and 6, 11 and 7, 11 and 8, 11 and 9, 11 and 10, 11 and 11, 11 and 12, 11 and 13, 11 and 14, 11 and 15
12.1 Warm Up
1. “H” for heads, “T” for tails, HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
2. “B” for blue, “Y” for yellow, “G” for green, “R” for red, BB, BY, BG, BR, YY, YB, YG, YR, GG, GB, GY, GR, RR, RB, RY, RG
3. BH, BT, YH, YT, GH, GT, RH, RT
12.1 Cumulative Review Warm Up
1. 4 33 4 33sin , cos , tan ,
7 7 33
7 7 33 33csc , sec , cot
4 33 4
θ θ θ
θ θ θ
= = =
= = =