Page 685 - Basic College Mathematics with Early Integers

662 C HAPTE R 9 I GEOMETRY

PRACTICE 1 Example 1 Find the volume and surface area of a rectangular box that is
Find the volume and surface 12 inches long, 6 inches wide, and 3 inches high.
area of a rectangular box that
is 7 feet long, 3 feet wide, and
.
4 feet high.

Solution: Let h = 3 in., l = 12 in., and w = 6 in.
V = lwh
#
#
V = 12 inches 6 inches 3 inches = 216 cubic inches
The volume of the rectangular box is 216 cubic inches.
SA = 2lh + 2wh + 2lw
= 2(12 in.)(3 in.) + 2(6 in.)(3 in.) + 2(12 in.)(6 in.)
= 72 sq in. + 36 sq in. + 144 sq in.
= 252 sq in.
The surface area of the rectangular box is 252 square inches.
Work Practice 1

Concept Check Juan is calculating the volume of the following rectangular
solid. Find the error in his calculation.
Volume = l + w + h
= 14 cm + 8 cm + 5 cm 5 cm
= 27 cu cm
8 cm
14 cm

PRACTICE 2 Example 2 Find the volume and surface area of a ball of radius 2 inches. Give
Find the volume and surface the exact volume and surface area. Then use the approximation
area of a ball of radius 22 for p.
1 7
centimeter. Give the exact
2
volume and surface area.Then 2 in.
22
use for p and approximate
7
the values.

Solution:
4 3
Answers V = pr Formula for volume of a sphere
3
1. V = 84 cu ft ; SA = 122 sq ft
4 3
1 11 V = # p(2 in.) Let r = 2 inches.
2. V = p cu cm L cu cm ; 3
6 21
32
1 = p cu in. Exact volume
SA = p sq cm L 3 sq cm
7 3
32 22 22 Copyright 2012 Pearson Education, Inc.
p
L # cu in. Approximate with .
Concept Check Answer 3 7 7
# #
Volume = l w h 704 11
= 14 cm # 8 cm 5 cm = or 33 cu in. Approximate volume
#
21 21
= 560 cu cm