MOP, MNO, PNO BCGF, CDHG, DHEA, EFGH. UPQV, VQSX, XSTY, YTRW, UWRP and pentagons UVXYW and PQSTR
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1 Answers for Lesson -, pp Exercises. 4, 6, 4; M, N, O, P; MN, MP, MO, NO, NP, OP; MNP, MOP, MNO, PNO 2. 8, 2, 6; A, B, C, D, E, F, G, H; AB, BC, CD, DA, AE, BF, CG, DH, EF, FG, GH, HE; quadrilaterals ABCD, ABFE, BCGF, CDHG, DHEA, EFGH. 0, 5, 7; P, Q, R, S, T, U, V, W, X, Y; UV, VX, XY, YW, WU, UP, VQ, XS, YT, WR, PQ, QS, ST, TR, RP; quadrilaterals UPQV, VQSX, XSTY, YTRW, UWRP and pentagons UVXYW and PQSTR ; ; ; Geometry Chapter 240
2 Answers for Lesson -, pp Exercises (cont.). two concentric circles 4. triangle 5. rectangle 6. a. b. Sample: 7. rectangle 8. square 9. rectangle 20. a b. Answers may vary. Sample: 2 cm 6 cm 6 cm 6 cm 2 cm 2 cm 2 cm 2 cm 2 cm 2. rectangle 22. rectangle 2. triangle 24. triangle 25. circle trapezoids Geometry Chapter 24
3 Answers for Lesson -, pp Exercises (cont.) 27. cone 28. sphere 29. cylinder attached to a cone Check students work. 6. a. A. icosahedron B. octahedron C. tetrahedron D. hexahedron E. dodecahedron 7. A b. regular triangular pyramid, cube c Check students work. 44. Check students work Geometry Chapter 242
4 Answers for Lesson -, pp Exercises (cont.) Geometry Chapter 24
5 Answers for Lesson -2, pp Exercises. 726 cm cm 29 cm 6.5 cm 9 cm ft 2 6 ft 6 ft 6 ft. (80 2!2) in. 2 or about 25. in a. right hexagonal prism b. 240 cm 2 c. 48! cm 2 4 in. 8 in. d. Q240 48!R cm ft 2 ; 220 ft in. 2 ; 08 in cm 2 ; 2 cm p cm p cm p in cm in in m cm cm cm 2 4 in. 4!2 in. 4!2 in. Geometry Chapter 244
6 Answers for Lesson -2, pp Exercises (cont.) 8. A cylinder and a prism both have two bases. The bases of a cylinder are circles, and the bases of a prism are polygons mm Answers may vary. Sample: 4 cm cm 4 cm 2. a. 94 units 2 b. 76 units 2 c. 4: d. 48 units 2 ; 752 units 2 ;4 : e. The surface area becomes 4 times as large. 22. A in about 75.5 in a. 7 units b. 96p units a. A(, 0, 0); B(, 5, 0); C(0, 5, 0); D(0, 5, 4) b. 5 c. d. 4 e. 94 units 2 4 cm 27. cylinder of radius 4 and height 2; 48p units cylinder of radius 2 and height 4; 24p units cylinder of radius 2 and height 4; 24p units 2 0. cylinder of radius 4 and height 2; 48 units 2 p Geometry Chapter 245
7 Answers for Lesson -2, pp Exercises (cont.). a. Lateral area is doubled. b. Surface area is more than doubled. c. S.A. 2pr 2 2prh; if r doubles: S.A. 2(4pr 2 2prh). Since r is squared, surface area is more than doubled. 2. a. r.2 in.; h 6 in. b. about 54.0 in. 2. ( p) cm 2 4. (84 20 p) m 2 5. (220 8 p) in h 6 m; r m 7. a. 0, 8, 2, 6, b. 728 in. 2 Geometry Chapter 246
8 Answers for Lesson -, pp Exercises. 408 in m in m cm m ,08 ft p cm 2 9. p ft p cm in m cm 2 4. Answers may vary. Sample: PT PR, since PR is a hyp. in PTR. m&pcr m&pbr (since PCB is isosc.) and m&pbr m&prc, so m&pcr m&prc. Therefore, PR PC. 5. Altitude; altitude; the altitude is shorter because it is one leg of a right with the lateral edge as the hyp., and is steeper because it rises the same vert. distance over less horiz. distance in ft cm cm in in. 22. Answers may vary. Sample: 6 cm 64 cm ft 2 0 in. 4 in. 4 cm 4 cm Geometry Chapter 247
9 Answers for Lesson -, pp Exercises 24. Cylinder: the lateral area of the 2 cones is 0p in. 2 and the lateral area of the cylinder is 48p in (, r)rp pr, pr 2, which is the lateral area plus the circular base area. This formula may require fewer keystrokes and doesn t use exponents. S.A. pr 26. a., r 27. A b. r m ft m 2. L.A. 0 in. 2, h < 4.8 in.,, 5 in. 2. s 2 m, L.A. 240 m 2, S.A. 84 m 2. s 2 ft, h < 4.9 ft, S.A. 24 ft 2 4. s 8 cm,, < 7.4 cm, h < 6.2 cm cm 6. about 6.5 cm 2 7. cone with r 4 and h ; 6p 8. cone with r and h 4; 24p 9. cylinder with cone-shaped hole; 60p 40. cylinder with cone-shaped hole; 48p 4. 00!5 cm 2 ; 00!5 00 cm p!5 cm 2 ;25p!5 25p cm p/ "p 2 / 2 4p(S.A.) 2p Geometry Chapter 248
10 Answers for Lesson -4, pp Exercises. 26 ft in.. 80 m 4. 4 cm 5. about cm ft mm in p in. ; in p cm ; 25.7 cm. 7.5p m ; 7.8 m cm. 445 in. 4. a. 28 ft b. 747 lb in. 6. Answers may vary. Sample: 2 cm by 4 cm by 0 cm; 4 cm by 4 cm by 5 cm cm 8. 5 in ft 20. about.4 ft pots ft 2. a. 809,7 ft b.,98,88,76 in. c. 6,052,765 gal 24. Reword as If two plane figures have the same height and the same width at every level, then they have the same area units cm 27. cm 28. A 29. Bulk; cost of bags $67, cost of bulk is $6. 0. cylinder with r 2 and h 4; 6 units p Geometry Chapter 249
11 Answers for Lesson -4, pp Exercises (cont.). cylinder with r 4 and h 2; 2p units 2. cylinder with r 2 and h 4; 6p units. cylinder with r 5, h 2, and a hole of radius ; 48p units cm in. 6. a. 70 in. 2 b. 528 in. 2 c. 756 in. d. 476 in. 7. a. circumference 8 in. and height in.: V 6.2 in. ; circumference in. and height 8 in.: V 8.8 in. ; one is about 0.8 times the volume of the other. b. about 6.5 in. by.0 in cm 9. 4 units 40. The volume of B is twice the volume of A. 2 2 Geometry Chapter 250
12 Answers for Lesson -5, pp Exercises. about 2, ft cm. 296 in m 5. about 44.7 cm in m 8. about 6.6 m 9. about 74.5 mm 0. about ft 6. p ft ; 7 ft 2. p in. ; 2 in p in. ; 5 in. 4. about 66.4 cm 5. about 4.7 cm 6. 2 in cm 8. 0,68 ft 9. They are equal; both volumes are pr 2 h. 20. a. 6,2,000 ft b. 284 ft ! cm 25. B cube: 8 units, cone: p units, pyramid: units 27. a. 20p ft b. 60p ft c. 240p ft 28. cone: 24.6 in. ; prism: 240 in. ; pyramid: 256 in. 29. cone with r 4 and h ; 6p 0. cone with r and h 4; 2p 22 8 Geometry Chapter 25
13 Answers for Lesson -5, pp Exercises (cont.). cylinder with r 4, h, with a cone of r 4, h removed from it; 2 2. cone with r 4, h 5, with a cone of r, h cut off the top, and a cylinder of r, h 4 cut out of its center; 24p. a. The frustum has vol. V R 2 H r 2 h (R 2 H r 2 p p p h). Now if h H h is the frustum s height, V p(r 2 (h h) R 2 h) p (R 2 h h(r 2 r 2 )). By similar >,, rh R 2 r or h. Simplifying, V ph (r 2 rr R 2 ). b. about in. 4. a. about 47. m b. about 76.7 m 2 c. about 89.6 m p 5. about 6.2 cm 6. about 8.8 cm h r 5 h h R Geometry Chapter 252
14 Answers for Lesson -6, pp Exercises. 900p m p in p mm ,000p yd p mm p cm p in cm in cm in p ft ; 524 ft. 288p cm ; 905 cm 4. p in. ; 767 in. 5. p cm ; 245 cm p yd ; 728 yd p m ; 0 m in m cm 2 2. S.A. 08 cm 2 ; V 08 cm 22. a. sphere of radius 4 b. p units c. 64p units 2 2. Yes; the volume of the frozen yogurt is cm, and the volume of the cone is 64 cm p p. 24. C Answers may vary. Sample: (5, 0, 0), (0, 5, 0), (0, 0, 5), ( 5, 0, 0), (0, 5, 0), (0, 0, 5) 26. A: on; B: inside; C: outside lb Geometry Chapter 25
15 Answers for Lesson -6, pp Exercises (cont.) in. sphere; the volume of the three spheres is.5p and of the large sphere is 85 p p m 0. 6p in p ft 2. p mm p yd p cm p m 6. p mi 7. a. 457 p in. 2 b. 228 p in. c. in. 8. a. about 8.9 in. 2 b. The answer is less than the actual surface area since the dimples on the golf ball add to the surface area. 9. Answers may vary. Sample: sphere radius in.; cylinder radius in., height 4 in p cm 2 ; p cm p cm 2 ; p cm p cm 2 ; p cm 4. Answers may vary. Sample: You could lift the small ball because it weighs about 75 lb. The big ball would be much harder to lift since it weighs about 25 lb. 44. a. 6! in.;! in. b. 7.7 in. 45. r 7. cm, h 4. cm Geometry Chapter 254
16 Answers for Lesson -6, pp Exercises (cont.) 46. r 8.2 cm, h.4 cm cm a. Cube; explanations may vary. Sample: 4 " 4p " 4p If s pr, then s r. So 6s 2 6Q rr 2 5.6r 2 4pr 2. b. Answers may vary. Sample: Spheres are difficult to stack. 49. m m 5. 2 : Geometry Chapter 255
17 Answers for Lesson -7, pp Exercises. no 2. yes; : 2. yes; 2 : 4. no 5. yes; 2 : 6. no 7. 5 : : 7 9. : : in m. 24 ft in m yd toothpicks oz 9. a. It is 64 times the smaller prism. b. It is 64 times the smaller prism. 20. a. 2:5 b. 4:25 c. 8:25 2. No; explanations may vary. Sample: If size refers to the vol., then the new clock should be at the weight. 22. Yes; 60;. 2. about 000 cm 24. No; an increase in the lengths of sides does not create prop. ratios unless the box is a cube. 25. Answers may vary. Sample: A sphere has only one measure, r, so there s only one possible ratio ft 27. a. : b. 9 : a. : 4 b. 2 : in. 0. :4; :8 4 0 Geometry Chapter 256
18 Answers for Lesson -7, pp Exercises (cont.). 9 : 25; 27 : : 9; 4 : : 8; 25 : a. 44 coats b. 728 meals 5. a. 00 times b. 000 times c. His weight is 000 times the weight of an average person, but his bones can only support 600 times the weight. 6. a. 84 cm b. 6: c. pyramid A: 84 cm 2 ; pyramid B: 24 cm 2 7. a. 4 :;8 : b. Let r radius, / slant height of small cone. / 5r :4/ 4r;/ 5r : / r c. 7 :8;7 : Geometry Chapter 257
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