Computing Volume of Three-Dimensional Solids (Part Two) Cube

in Aviation Mathematics

A cube is a solid with six square sides. [Figure 1-25] A cube is just a special type of rectangular solid. It has the same formula for volume as does the rectangular solid which is Volume = Length × Width × Height = L × W × H. Because all of the sides of a cube are equal, the volume formula for a cube can also be written as:

Volume = Side × Side × Side = S3

Example: A large, cube-shaped carton contains a shipment of smaller boxes inside of it. Each of the smaller boxes is 1 ft × 1 ft × 1 ft. The measurement of the large carton is 3 ft × 3 ft × 3 ft. How many of the smaller boxes are in the large carton? First, substitute the known values into the formula.

V = L × W × H
= 3 ft × 3 ft × 3 ft
= 27 cubic feet of volume in the large carton

Since each of the smaller boxes has a volume of 1 cubic foot, the large carton will hold 27 boxes.

Figure 1-25. Cube.

Figure 1-25. Cube.