Answers to Geometry Unit 5 Practice

Transcription

1 Lesson 0- Answers to Geometry Unit 5 Practice. a. Rectangle; Sample answer: It has four right angles. b. length: units; width: 9 units A 5 bh 7 units. 96 units. a. Parallelogram; Sample answer: Opposite sides are congruent. b. PQ 5 units, QR 5 0 units, RS 5 units, SP 5 0 units 44 units 96 units 4. A ft Lesson units 7. a. 6 or 6.5 cm b. 6 or 7.7 units 5 or 4.8 in D or 57.8 cm 0. perimeter:.97 units; area: 60 Lesson 0-. a. 08 cm b. 50 or 70.7 cm or 9.5 in. 70 cm. a. 78 cm b. 6 in. 40 in. 8 units. 4 in units 5. C Lesson - 6. a. b. m W 5 958, m X 5 988, m Y 5 88, m Z C 8. a. 68 b a. 708, 408 b. 558, Lesson -. a. 08 b a. 58 b D 4. a. 908 b e Lesson - 6. a.. cm b.. cm 80 cm cm 7. a. 9.8 cm b. 4. cm 6.4 cm 08.7 cm 8. a. 6. cm b. 9. cm 0.9 cm 96.8 cm areaof octagon asn e. areaof pentagon 5 5 (0.5)(0.9)(9.)(8) asn (0.5)(6.)(9.)(5) C 05 College Boar All rights reserve A

2 0. a. side: 0 units; height: 0 units b. 5 units 5 6 units 50 units Lesson -. a. 0π cm b. 5π cm 0 π cm 50π cm. B π. or in.; 6.8 in. π π 4. a. 660π in. or 07.5 in. b revolutions 5. a. 47.5π units b. 9π units Lesson. 6. a. 6π in. b π in. 80 π 8 7. a. 7.0 cm Lesson. 4. a. 608 b e a. π 4 b. π π 5π 6 π e. 4. a. 8π units b. 0 units 5 : 5 : D 45. a. Dilate circle B by a factor of.5. b. Dilate circle A by a factor of : 4 5 : 6 b. π 90 cm a. b. 08 cm π 8π cm π 4 cm 5π 6 in. 800 cm π 5π cm 9 9. a. 5. units 40. B b. π units Lesson a. rectangle b. triangle rectangle, 4 triangles 5 vertices, 5 faces, 8 edges 47. a. regular pentagon b. rectangle regular pentagons, 5 rectangles 0 vertices, 7 faces, 5 edges B 50. Yes; Sample answer: V E F 5, so for this polyhedron F 5 9. An octagonal pyramid satisfies these conditions. 05 College Boar All rights reserve A

3 Lesson - 5. C 5. a. a circle b. a rectangle Yes; if the plane is perpendicular to the bases and just touches the curved surface, then the cross section is a segment. Sample answer: For every plane that intersects the bases and is perpendicular to them, the cross section is a rectangle. Every rectangle has the same height, which is the height of the cylinder. The rectangles have different widths; the greatest width is the diameter of the base, and the cross section has that width if the plane contains the center of the base. 5. The net consists of two congruent circles and a rectangle. The circumference of the circle is the same as the side of the rectangle that it touches. 54. a. point A b. XZ, XW, or XY the length of ZWY BC 55. a. 6π cm b. 6π cm Lesson a. Yes, the plane contains the center of the sphere. b. No, the plane does not contain the center of the sphere. 57. The plane is tangent to the sphere. 58. a. line m b. line line n line p 59. C 60. a. a cone b. the height of the cone the radius of the base the slant height Lesson 4-6. a. 8.8 cm b. 8.8 cm by 6 cm circle: 8. cm ; rectangle:.8 cm 69.4 cm 6. a. 5 in. b. 4 in. 70 in. 48 in. e. 66 in. 6. a. 500 cm b. 60 cm 64. B 65. a. 40π cm b. 400 cm (00 4π) cm (600 π) cm Lesson m in. 68. D 69. a. 5 cm b. 0 in. 70. a. 40. ft b. 4 min Lesson 5-7. C 7. a. 44π units b. 80π units 4π units 9 units 7. a. 40π cm b. 64π in. 64π( ) cm 6 cm 05 College Boar All rights reserve A

4 74. a. 4π cm b. 40π cm 6 cm 4π 6 cm e. (44π 4π 6) cm 75. a. 4.4 cm b cm Lesson D 77. a. 56 cm b. slant height: 5 cm; volume: 48 cm 7 in. 4 units 78. a. h cm b. r cm 5.0 cm 6.5 cm 79. a. The cone; Sample answer: The heights are equal, and the area of the base of the cone is greater than the area of the base of the pyrami b. (0π 40) cm ; 7 cm 80. D Lesson 5-8. a. 4. cm b. 0. g 8. a..8 cm b..77 cm 6.5 cm.7 g/cm 8. B kg/m 85. a..5 kg/m b. 580 kg 55 m 0.55 kg/m Lesson A 87. a. 56π in. ; 804. in. b. 600π cm ; cm 9π 4 in. or.5π in. ; 7. in. 0.04π unit ; 0. unit 88. a. 96π cm b. 0 cm 0000π units π cm 89. a. 44π cm b. 88π cm 90. r in. Lesson cm 048π 9. a. cm b. 56π cm 9π cm 9. a. 7.8 in. b. 4.6 in in. 9.9 in. 94. B 95. a. cone: 9π units ; hemisphere: 8π units ; cylinder: 7π units b. : : vol. cone The results are the same: vol. hemi. 5 vol. hemi. and 5 vol. cyl. Lesson B a. Sample answer: For any other great circle that contains point A, the antipode for A is the other intersection of the two great circles. b. Sample answer: If A is one endpoint of a diameter of the sphere, the antipode for A is the other endpoint of that diameter College Boar All rights reserve A4

5 98. Sample answer: The term line in Euclidean geometry is an undefined term. In spherical geometry, line refers to any great circle on a sphere. 99. a. Sample answer: The dashed object is not a great circle so it is not a line in spherical geometry. Since it is not a line, it cannot be considered as a parallel line to the great circle. b. Sample answer: 00. B Lesson 7-0. a. 79 ft, 78 ft b. 7 : 64 : 4 Sample answer: The ratio of the volumes is the cube of the ratio of the side lengths. 0. a. 88π cm b. 97π cm 8 : 7 sphere A: 44π cm ; sphere B: 4π cm e. 4 : in. 56π 04. a. units 4π b. units 64 : Sample answer: The radius of the largest sphere is four times the radius of the smallest sphere, and the ratio of the volumes is the cube of the ratio of the radii. 05. D Lesson a..5π cm b. 0π cm : 8 cylinder : 7π cm ; cylinder : 8π cm e. : a. The volume is divided by 4. b. The volume is divided by. 08. B 09. a. A 5 96 cm ; V 5 64 cm b. 84 cm 0. a. The new area is 6 or 64% of the original area. 5 b. The new volume is 64 or 5.% of the 5 original volume. 05 College Boar All rights reserve A5