Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK Preparing for the Regents Examination Geometry, AK
16 240 17 144 √ 3 cm 2 18 432 √ 3 ft 3 11-9 Cones (pages 283–284) 1 Lateral area: 60; total area: 96; volume: 96 2 Lateral area: 20; total area: 36; volume: 16 3 Lateral area: 136; total area: 200; volume: 320 4 Lateral area: 80; total area: 105 5 Lateral area: 135 cm 2 ; volume: 324 cm 3 6 Lateral area: 260 in. 2 ; total area: 360 in. 2 ; volume: 800 in. 3 7 r 3 8 V 36 9 V 16 10 V 12 11 r 10 12 1 _ 3 base height 13 equal 14 three times 15 one-third 16 No, because the slant height is always greater than the radius. 17 4 : 1 18 h 8 19 28.5 in. 3 20 Volume: 3,056 _ 3 1,018.67 in. 3 ; lateral area: 300 in. 2 21 144 √ 3 22 60 11-10 Spheres (pages 287–288) 1 a r 10.5 ft b r 6.2 ft c r 2.9 ft 2 a r 5 mi b r 2 √ 5 4.5 mi c r 4 mi d r 1.6 mi 3 a 288 in. 3 b 36 ft 3 c 972,000 mi 3 d 1 _ yd 6 3 e 4 _ 3 m 81 4 r 7 in. 5 Surface area: 100 cm 2 ; volume: 500 _ 3 cm 3 6 Surface area: 192 in. 2 ; volume: 256 √ 3 in. 3 7 Volume: 1,679,616,000 cubic miles; surface area: 4,665,600 square miles 8 63,361,600 square miles 9 1,000,000 times 10 r 5 11 r 3 12 9 : 25 or 9 _ 25 13 a 2 : 5 or 2 _ 5 14 a 2 _ b 3 4 _ 9 15 a m 2 : n 2 b m 3 : n 3 16 64 _ 27 17 108 ounces 18 1,458 lb. b 4 : 25 or 4 _ 19 a r √ 2 _ b r 4 _ 20 r _ √ 24 √ 21 a 1 _ ft 6 3 b 4 _ ft 3 3 c 4.5 ft 3 22 64 23 h 4r 24 : 6 or _ 6 25 2 : 3 or 2 _ 3 26 They are equal. Lateral area of cylinder 16 in. 2 Surface area of sphere 16 in. 2 25 Chapter Review (pages 289–290) 1 (4) 216 in. 2 2 False 3 False 4 True 5 True 6 False 7 False 8 False 9 False 10 True 11 True 12 a 8 vertices, 6 faces, 12 edges b 6 vertices, 5 faces, 9 edges c 8 vertices, 6 faces, 12 edges d 10 vertices, 7 faces, 15 edges 13 a Surface area: 216, volume: 432 b Surface area: 90, volume: 100 c Surface area: 52 ft 2 , volume: 24 ft 3 Chapter Review 71
14 47.5 in. 2 15 h 4 in. 16 25 cm 3 17 The cylinder formed by spinning the rectangle about the shorter side is 96 cm 3 greater in volume. r 6 and h 8, V 288 cm 3 r 8 and h 6, V 384 cm 3 18 36 9 √ 3 in. 2 19 36 √ 3 in. 3 20 144 √ 3 cm 3 21 480 22 156 in. 2 23 √ 65 in. Ratios, Proportion, and Similarity 12-1 Ratio and Proportion (pages 294–295) 1 No 2 Yes 3 No 4 Yes 5 a 3 _ 2 b 2 _ 5 c 3 _ 5 d 5 _ 3 6 77 7 15 8 9 9 15 10 5 72 Chapter 12: Ratios, Proportion, and Similiarity 24 100 ft 3 25 60 ft 2 26 Lateral area: 15 in. 2 ; volume: 12 in. 3 27 r 3 in.; volume: 36 in. 3 28 Surface area: 40,000 cm 2 Volume: 4,000,000 _ 3 cm 3 or 1,333,333 1 _ cm 3 3 29 Surface area: 4 ft 2 ; volume: 4 _ ft 3 3 30 r 8 _ √ meters 31 5 _ inches or 2.5 inches 2 32 40.57 41 scoops 11 44 12 15 13 39 14 mt _ a 15 2ma _ r 16 4ar _ t 17 9 18 8 19 15 20 4 √ 3 21 3 √ 11 22 5 √ 3 23 6 √ 2 24 4 √ 6 25 1 _ 10 26 1 _ or _ √ 3 3 √ 3 9 CHAPTER 12
- Page 23 and 24: 5-3 Isosceles and Equilateral Trian
- Page 25 and 26: 12. −−− HG −−− DC 13.
- Page 27 and 28: 5 1. −− FG is the perpendicular
- Page 29 and 30: Chapter Review (pages 84-85) Note:
- Page 31 and 32: 20 Use constructing congruent angle
- Page 33 and 34: 6-3 Line Reflections and Symmetry (
- Page 35 and 36: 11 A(0, 8), B(2, 2), C(6, 4) (8) 10
- Page 37 and 38: 5 (3) (x, y) → (x, 2y) 6 (1) tran
- Page 39 and 40: 11. mABC mADC 12. 2mABD 2mADB 13.
- Page 41 and 42: 6. mDAB mCAD mDCB mACD 7. mCAB
- Page 43 and 44: g e 17 a _ f d b Undefined c a _
- Page 45 and 46: 5 BIG is isosceles because it has t
- Page 47 and 48: ___ 27 a M KA (5, 1), M ___ AT (4
- Page 49 and 50: 8 106 9 mA 75, mC 67 10 57 11 60
- Page 51 and 52: 9-5 The Sum of the Measures of the
- Page 53 and 54: 9-7 The Converse of the Isosceles T
- Page 55 and 56: 12 1. ___ CE ___ BA , ___ BD ___
- Page 57 and 58: 12 a mx 45, my 45 b mx 98, my 8
- Page 59 and 60: Quadrilaterals 10-2 The Parallelogr
- Page 61 and 62: 7. MAD RCB 8. MAD RCB (SAS SAS)
- Page 63 and 64: 5. RSQ TSV (Vertical angles) 6. QR
- Page 65 and 66: 3 4x 2 3x 3 x 5 RS 18 4 Perime
- Page 67 and 68: Note: Since there are many variatio
- Page 69 and 70: 28 Enclose PAT in a large rectangle
- Page 71 and 72: Geometry of Three Dimensions 11-1 P
- Page 73: 11-6 Volume of a Prism (pages 269-2
- Page 77 and 78: 14 a 3 : 2 b QR 10, RS 20, ST 12
- Page 79 and 80: 4. A A 5. ADE ABC b (AA) AC _ AB
- Page 81 and 82: 12 7 √ 2 13 4 14 5 √ 3 15 x
- Page 83 and 84: 13-2 Arcs and Chords (pages 350-351
- Page 85 and 86: 27 1. Common external tangents, −
- Page 87 and 88: 8. mHCT 1 _ m 2 TH mCHT 1 _ CT 2
- Page 89 and 90: 16 a (2 √ 2 , 2 √ 2 ), (2 √
- Page 91 and 92: 15 a Use constructing a congruent a
- Page 93 and 94: 5 Two horizontal lines y 11 and y
- Page 95 and 96: Each review has a total of 58 possi
- Page 97 and 98: Part III For each question, use the
- Page 99 and 100: Chapters 1-3 (pages 438-441) Part I
- Page 101 and 102: Part IV For each question, use the
- Page 103 and 104: 16 Score Explanation 4 a 91, b 35
- Page 105 and 106: Chapters 1-5 (pages 446-449) Part I
- Page 107 and 108: Part IV For each question, use the
- Page 109 and 110: 20 Score Explanation 6 The followin
- Page 111 and 112: 17 Score Explanation 4 The followin
- Page 113 and 114: Part II For each question, use the
- Page 115 and 116: Part IV For each question, use the
- Page 117 and 118: Part III For each question, use the
- Page 119 and 120: Chapters 1-9 (pages 461-463) Part I
- Page 121 and 122: 19 Score Explanation 6 The followin
- Page 123 and 124: 12 Score Explanation 2 31, and an a
16 240<br />
17 144 √ 3 cm 2<br />
18 432 √ 3 ft 3<br />
11-9 Cones<br />
(pages 283–284)<br />
1 Lateral area: 60; total area: 96;<br />
volume: 96<br />
2 Lateral area: 20; total area: 36;<br />
volume: 16<br />
3 Lateral area: 136; total area: 200; volume:<br />
320<br />
4 Lateral area: 80; total area: 105<br />
5 Lateral area: 135 cm 2 ; volume: 324 cm 3<br />
6 Lateral area: 260 in. 2 ; total area: 360 in. 2 ;<br />
volume: 800 in. 3<br />
7 r 3<br />
8 V 36<br />
9 V 16<br />
10 V 12<br />
11 r 10<br />
12 1 _<br />
3 base height<br />
13 equal<br />
14 three times<br />
15 one-third<br />
16 No, because <strong>the</strong> slant height is always<br />
greater than <strong>the</strong> radius.<br />
17 4 : 1<br />
18 h 8<br />
19 28.5 in. 3<br />
20 Volume: 3,056 _<br />
3 1,018.67 in. 3 ; lateral area:<br />
300 in. 2<br />
21 144 √ 3<br />
22 60<br />
11-10 Spheres<br />
(pages 287–288)<br />
1 a r 10.5 ft b r 6.2 ft c r 2.9 ft<br />
2 a r 5 mi b r 2 √ 5 4.5 mi<br />
c r 4 mi d r 1.6 mi<br />
3 a 288 in. 3 b 36 ft 3<br />
c 972,000 mi 3 d 1 _ yd<br />
6 3<br />
e 4 _ 3<br />
m<br />
81<br />
4 r 7 in.<br />
5 Surface area: 100 cm 2 ; volume: 500 _ 3<br />
cm<br />
3<br />
6 Surface area: 192 in. 2 ; volume: 256 √ 3 in. 3<br />
7 Volume: 1,679,616,000 cubic miles; surface<br />
area: 4,665,600 square miles<br />
8 63,361,600 square miles<br />
9 1,000,000 times<br />
10 r 5<br />
11 r 3<br />
12 9 : 25 or 9 _<br />
25<br />
13 a 2 : 5 or 2 _<br />
5<br />
14 a 2 _<br />
b<br />
3<br />
4 _<br />
9<br />
15 a m 2 : n 2 b m 3 : n 3<br />
16 64 _<br />
27<br />
17 108 ounces<br />
18 1,458 lb.<br />
b 4 : 25 or 4 _<br />
19 a r √ 2 _<br />
b r 4 _<br />
20 r _ √ 24<br />
<br />
√ <br />
21 a 1 _ ft<br />
6 3 b 4 _ ft<br />
3 3 c 4.5 ft 3<br />
22 64<br />
23 h 4r<br />
24 : 6 or _<br />
6<br />
25 2 : 3 or 2 _<br />
3<br />
26 They are equal.<br />
Lateral area of cylinder 16 in. 2<br />
Surface area of sphere 16 in. 2<br />
25<br />
Chapter Review (pages 289–290)<br />
1 (4) 216 in. 2<br />
2 False<br />
3 False<br />
4 True<br />
5 True<br />
6 False<br />
7 False<br />
8 False<br />
9 False<br />
10 True<br />
11 True<br />
12 a 8 vertices, 6 faces, 12 edges<br />
b 6 vertices, 5 faces, 9 edges<br />
c 8 vertices, 6 faces, 12 edges<br />
d 10 vertices, 7 faces, 15 edges<br />
13 a Surface area: 216, volume: 432<br />
b Surface area: 90, volume: 100<br />
c Surface area: 52 ft 2 , volume: 24 ft 3<br />
Chapter Review 71
Change language