Geometry RBC A answers - d3jc3ahdjad7x7.cloudfront.net€¦ · Sample answer: To find the area of the triangle, ... 1.5 meters. 11 ... 11.4 Puzzle Time

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 ≈


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.


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


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

≈°


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


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


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.


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


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.


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


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.


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 ≈


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


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


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° ≈


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


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


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


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


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.


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


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


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


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


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

= = =

= = =

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Geometry RBC A answers - d3jc3ahdjad7x7.cloudfront.net€¦ · Sample answer: To find the area of the triangle, ... 1.5 meters. 11 ... 11.4 Puzzle Time