Preparing for the Regents Examination Geometry, AK

11-6 Volume of a Prism
(pages 269–270)
1 288
2 15,625 m 3
3 a Volume: 105 cm 3 ; surface area: 142 m 2
b Volume: 3,600 in. 3 ; surface area: 1,500 in. 2
c Volume: 48 ft 3 ; surface area: 88 ft 2
4 147
5 a 2 b 6 c 4
d 5 e 3
6 14
7 1 _
2
8 Volume: 1,920 ft 3 ; surface area: 992 ft 2
9 1
10 Volume: 2,197 ft 3 ; diagonal: 13 √ 3 ft
11 30 inches
12 480 cm 3
13 9
14 2.7 ft
15 x √ 3
16 81 √ 3
17 Volume: 343; surface area: 294
18 24 √ 3 in. 3
19 Volume is ten times as large.
20 a Each solid has a volume of 360 √ 3 cubic
units.
b triangular prism 360 square units,
hexagonal prism 120 √ 6
21 Diagonal, d √
l 2 w 2 h 2 , so d 2
l 2 w 2 h 2 . Multiply by four, so that
4 d 2 4 l 2 4 w 2 4 h 2 .
11-7 Cylinders
(pages 273–274)
1 (3) 6 inches
2 h 11
3 V _
9
4 r 1 _
4
5 h 1 _
6 a 112 cm 2 b 136.5 cm 2 c 196 cm 3
7 a 96 in. 2 b 168 in. 2 c 288 in. 2
8 a 24 in. 2 b 26 in. 2 c 12 in. 2
9 a 6 m 2 b 14 m 2 c 6 in. 2
10 a r 3 b r 4
70 Chapter 11: Geometry of Three Dimensions
11 A cylinder with a radius of 8 and a height of
12 has a volume of 768. A cylinder with a
radius of 12 and a height of 8 has a volume
of 1,152. Their difference is 384.
12 38 pounds
13 r 3.4
14 h 29.4
15 a 64 b The volume is twice as
large; 128
c 32 d The lateral area stays
the same; 32.
16 a Doubled b Volume is 1 _ of the
4
volume original.
17 Yes. The volume of the glass with a diameter
of 2.4 is 1.44. Double the volume is 2.88.
The volume of the second glass is 2.89,
which is greater than twice the volume of the
first glass.
18 False
19 True
20 Lateral surface area: 960 in. 2 ; volume:
3,840 in. 3
21 h 6,930 _
36
385
_
2
22 16 : 64 or : 4
23 a V 256 b V 512
c V 256 512
11-8 Pyramids
(pages 278–279)
1 234 cm 2
2 240 cm 2
3 1,152 in. 2
4 4,848 cm 3
5 57.2 in. 3
6 7.5 ft 3
7 48 √ 3
8 h 300 ft
9 h 6
10 279 ft 2
11 864 in. 3
12 120
13 a 180 25 √ 3 b 340
c 360 150 √ 3
14 9 √ 3
15 Volume of pyramid is 80. Volume of prism
is 240.