Education.com
Try
Brainzy
Try
Plus

Pre-Algebra Volume Help

based on 1 rating
By — McGraw-Hill Professional
Updated on Sep 22, 2011

Volume

The volume of a geometric figure is a measure of its capacity. Volume is measured in cubic units. Cubic units are abbreviated using 3 for the exponent:

  • 1 cubic inch = 1 in. 3
  • 1 cubic foot = 1 ft 3
  • 1 cubic yard = 1 yd 3

The basic geometric solids are the rectangular solid, the cube, the cylinder, the sphere, the right circular cone, and the pyramid. These figures are shown in Fig. 9-16.

Volume

Fig. 9-16.

Volume of a Rectangular Solid

The volume of a rectangular solid can be found by using the formula V = lwh, where l = the length, w = the width, and h = the height .

Example 1

Find the volume of the rectangular solid shown in Fig. 9-17 .

Volume

Fig. 9-17.

Solution 1

Volume

Volume of a Cube

The volume of a cube can be found by using the formula V = s 3 , where s is the length of the side .

Example 2

Find the volume of the cube shown in Fig. 9-18 .

Volume

Fig. 9-18.

Solution 2

Volume

Volume of a Cylinder

The volume of a cylinder can be found by using the formula V = πr 2 h, where r is the radius of the base and h is the height .

Example 3

Find the volume of the cylinder shown in Figure 9-19 . Use π = 3.14.

Volume

Fig. 9-19.

Solution 3

Volume

Volume of a Sphere

The volume of a sphere can be found by using the formula Volume , where r is the radius of the sphere .

Example 4

Find the volume of the sphere shown in Figure 9-20. Use π = 3.14.

Volume

Fig. 9-20.

Solution 4

Volume

Volume of a Right Circular Cone

The volume of a right circular cone can be found by using the formula Volume , where r is the radius of the base and h is the height of the cone .

Example 5

Find the volume of the cone shown in Fig. 9-21 . Use π = 3.14.

Volume

Fig. 9-21.

Solution 5

Volume

Volume of a Pyramid

The volume of a pyramid can be found by using the formula Volume , where B is the area of the base and h is the height of the pyramid. If the base is a square, use B = s 2 . If the base is a rectangle, use B = lw .

Example 6

Find the volume of the pyramid shown in Fig. 9-22 .

Volume

Fig. 9-22.

Solution 6

In this case, the base is a square, so the area of the base is B = s 2 .

Volume

Converting to Cubic Measurements

Sometimes it is necessary to convert from cubic yards to cubic feet, cubic inches to cubic feet, etc. The following information will help you to do this. To change:

  • cubic feet to cubic inches, multiply by 1728;
  • cubic inches to cubic feet, divide by 1728;
  • cubic yards to cubic feet, multiply by 27;
  • cubic feet to cubic yards, divide by 27.

Examples

Example 7

Change 18 cubic yards to cubic feet.

Solution 7

18 × 27 = 486 cubic feet

Example 8

Change 15,552 cubic inches to cubic feet.

Solution 8

15,552 ÷ 1728 = 9 cubic feet

Volume Practice Problems

Practice

1. Find the volume of a rectangular solid if it is 8 inches long, 6 inches wide, and 10 inches high.

2. Find the volume of a cube if the side is 13 feet.

3. Find the volume of a cylinder if the radius is 3 inches and its height is 7 inches. Use π = 3.14.

4. Find the volume of a sphere if its radius is 9 inches. Use π = 3.14.

5. Find the volume of a cone if its radius is 6 feet and its height is 8 feet. Use π = 3.14.

6. Find the volume of a pyramid if its height is 2 yards and its base is a rectangle whose length is 3 yards and whose width is 2.5 yards.

Answers

1. 480 in. 3

2. 2197 ft 3

3. 197.82 in. 3

4. 3052.08 in. 3

5. 301.44 ft 3

6. 5 yd 3

Practice problems for these concepts can be found at: Informal Geometry Practice Test.

Add your own comment