Answers to Eercises CAPTER 10 CAPTER 10 LESSON 10.1 CAPTER 10 CAPTER 24. Answers to Eercises 1. polyedron; polygonal; triangles 2. PQR, TUS. PQUT, QRSU, RPTS 4. QU,PT,RS 5. 6 cm 6. GYPTAN 7. point E 8. GE,YE,PE,TE,AE,NE 9. 1 cm 10. D 11. L 12. C 1. G 14. B 15. 16. E 17. A 18. J 19. J 20. M 21. 22. I 2. 25. 26. 2 2 27. true 28. False. Tis statement is true only for a rigt prism. 29. true 0. true 1. False. It is a sector of a circle. 2. true. false; countereample: 4. true 5. true 114 ANSWERS TO EXERCISES
6. See tale elow. Possile answers include tat te numer of lateral faces of an antiprism is always twice te numer for te related prism; tat te numer of vertices is te same for eac related prism and antiprism; and tat te numer of edges for a prism is tree times te numer of faces, wile for an antiprism, te numer of edges is twice te numer of faces. 7. Answer sould include te idea tat te painting disappears into te view out te window. Students migt also note te effect created y te cone-saped tower appearing similar to te road disappearing into te distance. 8. 8 9. 60 40. 0 41a. yes 41. yes 41c. no 41d. yes 6. (Lesson 10.1) Triangular Rectangular Pentagonal eagonal n-gonal prism prism prism prism prism Lateral 4 5 6... n faces Total 5 6 7 8... n 2 faces Edges 9 12 15 18... n Vertices 6 8 10 12... 2n Answers to Eercises Triangular Rectangular Pentagonal eagonal n-gonal antiprism antiprism antiprism antiprism antiprism Lateral 6 8 10 12... 2n faces Total 8 10 12 14... 2n 2 faces Edges 12 16 20 24... 4n Vertices 6 8 10 12... 2n ANSWERS TO EXERCISES 115
LESSON 10.2 1. 72 cm 2. 24 cm. 108 cm 4. 160 cm 502.65 cm 5. 6 cm 11.10 cm 6. 24 cm 1017.88 cm 7. See tale elow. 8. 960 in 9. QT cuic units 12 in. 4 in. 24 in. T Q 20. 21. true 22. false 2. r r r Answers to Eercises 10. sample answer: 2 12 8 in. 12 8 11. 2 12. r 1. 1 14. Margaretta as room for 0.5625 cord. Se sould order a alf cord. 15. 170 yd 16. 5100 l 17. 11,140 18. Te volume of te quilt in 1996 was 4000 ft. Te quilt panels were stacked 2 ft 8 in. ig. 19. 12 24. possile solution: prism Salt crystal 25. approimately 1.89 m 26. 12 62 7. (Lesson 10.2) Information aout eigt Rigt triangular Rigt rectangular Rigt trapezoidal Rigt ase of solid of solid prism prism prism cylinder 2 r 6, 2 7, 20 a. V d. V g. V j. V 8, r 480 cm 960 cm 1040 cm 180 cm 9, 2 12, 20. V e. V. V k. V 12, r 6 1080 cm 2160 cm 2520 cm 720 cm 8, 2 19, 2 c. V f. V i. V l. V 18, r 8 1656 cm 12 cm 5589 cm 1472 cm 116 ANSWERS TO EXERCISES
LESSON 10. 1. 192 cm 2. 84 cm 26.9 cm. 150 cm 4. 60 cm 5. 84 cm 26.9 cm 6. 84 cm 1206 cm 7. m cm 8. 2 cm 9. 24 cm ;29.6% 10. See tale elow. 11. V 1 M 2 ft 14. 78,75 grams 15. 48 in 16. 4 units 17. 144 cm 18. 40,200 gal; 44 40 min 19. 71 ft 20. 40 arrels 21a. 16 cm 2 21. 96 cm 2 21c. 80 cm 2 21d. 241 120 cm 2 22. A D' 1 2 C 4 D B 12. sample answer: 16 M 27 48 M 1. Mount Etna is larger. Te volume for Mount Etna is approimately 219 km,and te volume for Mount Fuji is approimately 169 km. D'' Possile answer: From te properties of reflection, 1 and 2 4. m1 m2 90, so m m4 90, and m1 m2 m m4 180. Terefore D, C,and D are collinear. 2a. Y (a c, d) 2. Y (a c, d) 2c. Y (a c e, d f ) Answers to Eercises 10. (Lesson 10.) Information aout eigt Triangular Rectangular Trapezoidal ase of solid of solid pyramid pyramid pyramid Cone 2 r 6, 2 7, 20 a. V d. V g. V j. V 6, r 120 cm 240 cm 260 cm 60 cm 9, 2 22, 20. V e. V. V k. V 8, r 6 240 cm 480 cm 24 80 240 cm cm 1, 2 29, 24 c. V f. V i. V l. V 17, r 8 884 cm 1768 cm 2856 cm 512 cm ANSWERS TO EXERCISES 117
Answers to Eercises LESSON 10.4 1. 58.5 in 2. 2 cm 55.4 cm. 15 cm 4. 11 cm 5. 5.0 cm 6. 8. 5 in. 2 2 11 in. 6.24 in ; 11 in. 2 2 8.5 in. 81.85 in Te sort, fat cylinder as greater volume. 7. 257 ft 8. 4 cm 9. e must refute te statement. 10. 1502 l 11. 192.4 gal 12. 1 min 1. Answers will vary, ut r 2 sould equal aout 14.4 in. 14. approimately 8 in 15. 100,000 m, or aout 14,159 m ; 16,528 loads 16. AB EC ecause te opposite sides of a parallelogram are congruent. EC BD ecause te diagonals of a rectangle are congruent. So, AB BD ecause ot are congruent to EC. Terefore, ABD is isosceles. 17. 8.2 cm 18. 96 19. 20. A 21a. A 21. S 21c. N 21d. S 21e. A D 45 45 45 45 C B 118 ANSWERS TO EXERCISES
LESSON 10.5 1. 675 cm 2. 6 cm 11.1 cm. 47 in 4. 1798.4 g 5. Te gold as mass 2728.5 g, and te platinum as mass 7529.8 g. Te solid cone of platinum as more mass. 6. 1.5 cm 7. 10.5 g/cm ;silver 8. 8000 cm 9. Te volume of te medallion is 160 cm.yes,it is gold, and te Colonel is wo e says e is. 10. 679 cm 11. approimately 19 l; 22 fis 12. 2 9 1. flowcart proof: QR SP Given R S AIA SM MR Given RMQ SMP ASA MQ MP CPCTC QMR PMS Vertical Angles M is te midpoint of PQ Definition of midpoint 14. 15 sides 15a. (1, ) 15. ( 1) 2 (y ) 2 25 16. 58; n 2 Answers to Eercises ANSWERS TO EXERCISES 119
Answers to Eercises 1. 6 cm 11.1 cm 2. 6 cm 0.5 cm LESSON 10.6. 9 2 cm 0.884 cm 4. 720 cm 2262 cm 5. 0 cm 94. cm 6. 456 cm 10,857 cm 7. 18 m 56.6 cm 8. No. Te volume of te ice cream is 85. cm, and te volume of te cone is 64 cm. 9. only 20 scoops 10. 14 8 m, or aout 155 m 11. Tey ave te same volume. 12. 9 in. 1. cm 14. 819 2 cm 8579 cm 15. 18 in, or aout 57 in 16. No. Te unused volume is 16 cm,and te volume of te golf all is 10.6 cm. 17. approimately 15,704 gallons; 5 days 18. litium 19. 1 ft 20. ABCD is a parallelogram ecause te slopes of CD and AB are ot 0 and te slopes of BC and AD are ot 5. B (, 5) y C (, 5) D (9, 5) A (, 5) 21. Tey trace two similar sapes, ecept tat te one traced y C is smaller y a scale factor of 1:2. 22. Te line traces an infinite ourglass sape. Or, it traces te region etween te two rances of a yperola. 2. w 110, 115, y 80 120 ANSWERS TO EXERCISES
LESSON 10.7 16. 1 2 1. V 972 cm 054 cm S 24 cm 2 1018 cm 2 2. V 0.972 cm.054 cm S.24 cm 2 10.18 cm 2. V 1152 cm 619 cm S 42 cm 2 157 cm 2 4. S 160 cm 2 502.7 cm 2 6 cm 268.1 cm 5. V 25 6. S 144 cm 2 452.4 cm 2 7. Area of great circle r 2. Total surface area of emispere r 2. Total surface area of emispere is tree times tat of area of great circle. 8. 2 gal 9. V 1 2 4 (1.8) 1 2 (1.8)2 (4.0) 10.68 m 2.57 m ; S 1 2 4(1.8) 2 1 2 2(1.8)(4.0) 1.68 m 2 42.98 m 2 10a. approimately 082 ft 2 10. 1 gal 10c. approimately 9568 usels 11. 15,200,000 km 2 12. Te total cost is $11.95. e will stay under udget. 1. 1.1% 14. 150 cm 471.2 cm 15. 1 4 17. 4 18. Te ratio gets closer to 1. 19a and 19. See tales elow. 20. AB CB and AD CD y te definition of romus, and BD BD ecause it is te same segment; terefore ABD CBD y SSS. By CPCTC, 2 and 1 4, wic sows tat BD isects ot ABC and ADC.Because all four sides of te romus are congruent, a similar proof can e used to sow tat ABC ADC and tus tat A and C are ot isected y diagonal AC. 21a. AB CB y te definition of romus and BE BE ecause it is te same segment. 1 2 y te Romus Angles Conjecture. Terefore, AEB CEB y SAS. 21. AE CE y CPCTC, so BD isects AC. 21c. 4 y CPCTC. Also, and 4 form a linear pair, so tey are supplementary. Because two angles tat are congruent and supplementary are rigt angles, and 4 are rigt angles. 21d. Because and 4 are rigt angles, te diagonals are perpendicular.you still need to sow tat AC isects BD. Use a proof similar to tat given in 21a to sow tat AEB AED.Ten, y CPCTC, BE DE, wic sows tat AC isects BD. Answers to Eercises 19a. (Lesson 10.7) n 1 2 4 5 6... n... 200 f(n) 2 1 4 7 10 1... n 5... 595 19. (Lesson 10.7) n 1 2 4 5 6... n... 200 f(n) 0 1 1 2 5 2 5 7... n 1 1 n 1... 99 2 01 ANSWERS TO EXERCISES 121
Answers to Eercises 1. A USING YOUR ALGEBRA SKILLS 10 2. P 2 2 or P 2. r V 4. c 2 a 2 5. a 2 SA l P 6. y 2 m 2 1 y 1 or y 2 m 2 m 1 y 1 7. v d t Te original formula gives distance in terms of velocity and time. 9 8. F C 5 2 Te original formula converts degrees Fareneit to degrees Celsius. 9. L g T 2 2 Te original formula gives te period of a pendulum (time of one complete swing) in terms of lengt and acceleration due to gravity. 10a. V F E 2 10. See tale elow. 11a. Te corresponding radii are approimately.6 cm,.0 cm,.02 cm, and 2.79 cm. 11. Te corresponding eigts are approimately 9.2 cm,10.49 cm,11.61 cm,and 12.70 cm. 11c. Te corresponding volumes are approimately 129 cm, 120 cm, 111 cm, and 104 cm. 11d. Answers will vary. Sample answer: Te cone wit slant eigt 10 cm as te widest radius, so a scoop of ice cream is least likely to fall off, and tat cone also as te greatest volume. 11e. Answers will vary. Sample answer: Te cone wit slant eigt 1 cm as te greatest eigt, so te cone appears igger even toug it as te same surface area as te oter cones; tat cone also as te smallest radius and smallest volume, so it could old less ice cream and still appear to e a igger cone. m 1 m 2 m f f 12a. A 5 12. average of 60: 1; average of 70: 56; average of 80: 81; average of 90: 106 (impossile) 10. (Using Your Algera Skills 10) Pentaedron eaedron Octaedron Decaedron Dodecaedron Numer of faces 5 6 8 10 12 Numer of edges 8 10 12 16 20 Numer of vertices 5 6 6 8 10 122 ANSWERS TO EXERCISES
CAPTER 10 REVIEW 1. Tey ave te same formula for volume: V B. 2. Tey ave te same formula for volume: V 1 B.. 6240 cm 4. 1029 cm 2 cm 5. 1200 cm 6. 2 cm 7. 100 cm 14.2 cm 8. 2250 cm 7069 cm 9. 12.8 cm 10. 7 cm 11. r 12 cm 12. r 8 cm 1. 960 cm 14. 9 m 15. 851 cm 16. four times as great 17a. V etra large 54 in V jumo 201.1 in V colossal 785.4 in 17. 14.5 times as great 18. Cylinder B weigs 8 times as muc as cylinder A. 19. 2129 kg; 9 loads spe re 20. 2r. V V (2r) 0.524. Tus, 52.4% of o te o is filled y te all. 21. approimately 58 yd 22. No. Te unused volume is 98 in,and te volume of te meatalls is 2 in. 2. platinum 24. No. Te all weigs 25 l. 25. 256 l 26. approimately in. 2 27. 8 m 0.2 m 28. 160 cuic units 4 r Answers to Eercises ANSWERS TO EXERCISES 12