Basic Mathematics for College Students

In practice, we do not find volumes of three-dimensional figures by counting
cubes. Instead, we use the formulas shown in the table on the preceding page. Note
that several of the volume formulas involve the variable. It represents the area of
the base of the figure.

B

9.9 Volume 803

Caution! The height of a geometric solid is always measured along a line

perpendicular to its base.

EXAMPLE (^2) Storage Tanks An oil storage tank is in the form of a
rectangular solid with dimensions 17 feet by 10 feet by 8 feet. (See the figure
below.) Find its volume.
Self Check 2
Find the volume of a rectangular
solid with dimensions 8 meters by
12 meters by 20 meters.
Now TryProblem 29
StrategyWe will substitute 17 for , 10 for , and 8 for in the formula
and evaluate the right side.
WHYThe variable represents the volume of a rectangular solid.
Solution
This is the formula for the volume of a rectangular solid.
Substitute 17 for l,the length, 10 for w,the width, and 8
for h,the height of the tank.
Do the multiplication.
The volume of the tank is 1,360 ft^3.

1,360

V 17 ( 10 )( 8 )

Vlwh

V

l w h Vlwh

17 ft

8 ft

10 ft

EXAMPLE (^3) Find the volume of the prism
shown on the right.
StrategyFirst, we will find the area of the base
of the prism.
WHYTo use the volume formula , we
need to know , the area of the prism’s base.
SolutionThe area of the triangular base of the
prism is square centimeters. To find
its volume, we proceed as follows:
This is the formula for the volume of a triangular prism.
Substitute 24 for B,the area of the base, and 50 for h,
the height.
Do the multiplication.
The volume of the triangular prism is 1,200 cm^3.

1,200

V 24 ( 50 )

VBh

1

2 (6)(8)^24

B

VBh

Self Check 3

Find the volume of the prism

shown below.

Now TryProblem 33

10 in.

12 in. 5 in.

50 cm

10 cm

6 cm 8 cm

Caution! Note that the 10 cm measurement was not used in the calculation

of the volume.

1

5

70

 8

1,360

2

2

4

 50

1,200