Basic Mathematics for College Students

802 Chapter 9 An Introduction to Geometry

EXAMPLE (^1) How many cubic inches are there in 1 cubic foot?
StrategyA figure is helpful to solve this problem. We will draw a cube and divide
each of its sides into 12 equally long parts.
WHYSince a cubic foot is a cube with each side measuring 1 foot, each side also
measures 12 inches.
SolutionThe figure on the right helps us
understand the situation. Note that each level
of the cubic foot contains cubic inches
and that the cubic foot has 12 levels. We can
use multiplication to count the number of
cubic inches contained in the figure. There are
cubic inches in 1 cubic foot. Thus,1 ft^3 1,728 in.^3.

12  12  12 1,728

12  12

Self Check 1

How many cubic centimeters are

in 1 cubic meter?

Now TryProblem 25

Cube Rectangular Solid Sphere

where is the length of a side where is the length, is where is the radius

the width, and is the height

Prism Pyramid

where is the area of the where is the area of the

base and is the height base and is the height

Cylinder Cone

or or

where is the area of the base, where is the area of the base,

his the height, and is the radius of the baser his the height, and is the radius of the baser

B B

V

1

3

V pr^2 h

1

3

VBh Vpr^2 h Bh

h

r

h

r

r

h

r

h

h h

B B

V

1

3

VBh Bh

h h

h h

h

s l w r

V

4

3

Vs^3 Vlwh pr^3

r

w

h

l

s

s

s

1 ft 12 in.

12 in.

12 in.

1 ft

1 ft