# Computing Volume of Three-Dimensional Solids (Part One) Rectangular Solid

Three-dimensional solids have length, width, and height. There are many three-dimensional solids, but the most common are rectangular solids, cubes, cylinders, spheres, and cones. Volume is the amount of space within a solid. Volume is expressed in cubic units. Cubic inches or cubic centimeters are used for small spaces and cubic feet or cubic meters for larger spaces.

Rectangular Solid

A rectangular solid is a three-dimensional solid with six rectangle-shaped sides. [Figure 1-24] The volume is the number of cubic units within the rectangular solid. The formula for the volume of a rectangular solid is:

Volume = Length × Width × Height = L × W × H

In Figure 1-24, the rectangular solid is 3 feet by 2 feet by 2 feet.

The volume of the solid in Figure 1-24 is = 3 ft × 2 ft × 2 ft = 12 cubic feet.

Figure 1-24. Rectangular solid.

Example: A rectangular baggage compartment measures 5 feet 6 inches in length, 3 feet 4 inches in width, and 2 feet 3 inches in height. How many cubic feet of baggage will it hold? First, substitute the known values into the formula.

V = L × W × H
= 5’6″ × 3’4″ × 2’3″
= 5.5 ft × 3.33 ft × 2.25 ft
= 41.25 cubic feet