Basic Mathematics for College Students

Chapter 9 Summary and Review 831

SECTION 9.9 Volume

The volume of a figure can be thought of as the

number of cubic unitsthat will fit within its boundaries.

Two common units of volume are cubic inches (in.^3 )

and cubic centimeters (cm^3 ).

DEFINITIONS AND CONCEPTS EXAMPLES

1 in.

1 in.

1 in.

1 cubic inch: 1 in.^3

1 cm

1 cm

1 cm

1 cubic centimeter: 1 cm^3

CARRY-ON LUGGAGE The

largest carry-on bag that Alaska

Airlines allows on board a flight

is shown on the right. Find the

volume of space that a bag that

size occupies.

This is the formula for the volume of a

rectangular solid.

Substitute 24 for l,the length, 17 for w,the

width, and 10 for h,the height of the bag.

Do the multiplication.

The volume of the space that the bag occupies is 4,080 in.^3.

4,080

V 24 ( 17 )( 10 )

Vlwh

Figure Volume Formula

Cube

Rectangular solid

Prism

Pyramid

Cylinder

Cone

Sphere V^43 pr^3

V^13 pr^2 h

Vpr^2 h

V^13 Bh*

VBh*

Vlwh

Vs^3

*Brepresents the area of the base.

Length: 24 in.

Width: 17 in.

Height: 10 in.

The volumeof a solid is a measure of the space it

occupies.

Caution! When finding the volume of a figure, only

use the measurements that are called for in the

formula. Sometimes a figure may be labeled with

measurements that are not used.

Find the volume of the prism shown here.

The area of the triangular base of the

prism is square feet. (The 5-

inch measurement is not used.) To find the

volume of the prism, proceed as follows:

This is the formula for the volume of a prism.

Substitute 6 for B,the area of the base, and 9 for h,

the height.

Do the multiplication.

The volume of the triangular prism is 54 ft^3.

 54

V 6 ( 9 )

VBh

1

2 (3)(4)^6

The letter Bappears in two of the volume formulas.

It represents the area of the base of the figure.

Note that the volume formulas for a pyramid and a

cone contain a factor of.

Cone:

Pyramid: V^13 Bh

V^13 pr^2 h

13

9 ft

3 ft 4 ft

5 ft

5 cm

5 cm

6 cm

Find the volume of the pyramid shown here.

Since the base is a square with each side

5 centimeters long, the area of the base is

5  5  25 cm^2.

This is the formula for the volume of a pyramid.

Substitute 25 for B,the area of the base, and 6

for h,the height.

Multiply the first and third factors:.

Complete the multiplication by 25.

The volume of the pyramid is 50 cm^3.

 50

1

25(2) 3 (6) 2

V

1

3

( 25 )( 6 )

V

1

3

Bh