Answers to Exercises. Answers to Exercises 24.
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1 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 E 17. A 18. J 19. J 20. M I 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
2 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 a. yes 41. yes 41c. no 41d. yes 6. (Lesson 10.1) Triangular Rectangular Pentagonal eagonal n-gonal prism prism prism prism prism Lateral n faces Total n 2 faces Edges n Vertices n Answers to Eercises Triangular Rectangular Pentagonal eagonal n-gonal antiprism antiprism antiprism antiprism antiprism Lateral n faces Total n 2 faces Edges n Vertices n ANSWERS TO EXERCISES 115
3 LESSON cm cm. 108 cm cm cm 5. 6 cm cm cm cm 7. See tale elow in 9. QT cuic units 12 in. 4 in. 24 in. T Q true 22. false 2. r r r Answers to Eercises 10. sample answer: in r Margaretta as room for cord. Se sould order a alf cord yd l , Te volume of te quilt in 1996 was 4000 ft. Te quilt panels were stacked 2 ft 8 in. ig possile solution: prism Salt crystal 25. approimately 1.89 m (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 cm 2160 cm 2520 cm 720 cm 8, 2 19, 2 c. V f. V i. V l. V 18, r cm 12 cm 5589 cm 1472 cm 116 ANSWERS TO EXERCISES
4 LESSON cm cm 26.9 cm. 150 cm cm cm 26.9 cm cm 1206 cm 7. m cm 8. 2 cm cm ;29.6% 10. See tale elow. 11. V 1 M 2 ft ,75 grams in units cm ,200 gal; min ft arrels 21a. 16 cm cm 2 21c. 80 cm 2 21d cm A D' 1 2 C 4 D B 12. sample answer: 16 M 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 m 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 cm 480 cm cm cm 1, 2 29, 24 c. V f. V i. V l. V 17, r cm 1768 cm 2856 cm 512 cm ANSWERS TO EXERCISES 117
5 Answers to Eercises LESSON in 2. 2 cm 55.4 cm. 15 cm cm cm in in in ; 11 in in in Te sort, fat cylinder as greater volume ft 8. 4 cm 9. e must refute te statement l gal min 1. Answers will vary, ut r 2 sould equal aout 14.4 in. 14. approimately 8 in ,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 cm A 21a. A 21. S 21c. N 21d. S 21e. A D C B 118 ANSWERS TO EXERCISES
6 LESSON cm 2. 6 cm 11.1 cm. 47 in g 5. Te gold as mass g, and te platinum as mass g. Te solid cone of platinum as more mass cm g/cm ;silver cm 9. Te volume of te medallion is 160 cm.yes,it is gold, and te Colonel is wo e says e is cm 11. approimately 19 l; 22 fis 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 sides 15a. (1, ) 15. ( 1) 2 (y ) ; n 2 Answers to Eercises ANSWERS TO EXERCISES 119
7 Answers to Eercises 1. 6 cm 11.1 cm 2. 6 cm 0.5 cm LESSON cm cm cm 2262 cm 5. 0 cm 94. cm cm 10,857 cm 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 m, or aout 155 m 11. Tey ave te same volume in. 1. cm cm 8579 cm 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 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: Te line traces an infinite ourglass sape. Or, it traces te region etween te two rances of a yperola. 2. w 110, 115, y ANSWERS TO EXERCISES
8 LESSON V 972 cm 054 cm S 24 cm cm 2 2. V cm.054 cm S.24 cm cm 2. V 1152 cm 619 cm S 42 cm cm 2 4. S 160 cm cm 2 6 cm cm 5. V S 144 cm 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 gal 9. V (1.8) 1 2 (1.8)2 (4.0) m 2.57 m ; S 1 2 4(1.8) (1.8)(4.0) 1.68 m m 2 10a. approimately 082 ft gal 10c. approimately 9568 usels ,200,000 km Te total cost is $ e will stay under udget % cm cm 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 n f(n) n (Lesson 10.7) n n f(n) n 1 1 n ANSWERS TO EXERCISES 121
9 Answers to Eercises 1. A USING YOUR ALGEBRA SKILLS 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 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 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 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 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 Numer of edges Numer of vertices ANSWERS TO EXERCISES
10 CAPTER 10 REVIEW 1. Tey ave te same formula for volume: V B. 2. Tey ave te same formula for volume: V 1 B cm cm 2 cm cm 6. 2 cm cm 14.2 cm cm 7069 cm cm cm 11. r 12 cm 12. r 8 cm cm m cm 16. four times as great 17a. V etra large 54 in V jumo in V colossal in times as great 18. Cylinder B weigs 8 times as muc as cylinder A kg; 9 loads spe re 20. 2r. V V (2r) 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 l 26. approimately in m 0.2 m cuic units 4 r Answers to Eercises ANSWERS TO EXERCISES 12
Perimeter, Area and Volume of Regular Shapes
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