Volumes of three-dimensional figures

Volumes of three-dimensional figures

The volume of a three-dimensional figure is obtained by multiplying its base area by height. A rectangular prism has a length, width and height. A cube has a length which is the same as its width and height. A cylinder has a base and height. Generally in finding the volume of a three-dimensional figure, multiply the base area by height.

Rectangular prisms

In finding the volume of a rectangular prism, multiply its base area by height. Also, you can multiply length by width by height.

Example 1

Find the volume of a rectangular prism of length 20 cm, width 10 cm and height 15 cm.

Solution

Volume of rectangular prism = length × width × height

= 20 cm × 10 cm × 15 cm

Thus, the volume of the rectangular prism is 3,000 cm³

Cubes

A cube is similar to a rectangular prism. The only difference is that a cube has all its sides equal. That is length, width and height are all equal. In finding the volume of a cube shown in the following figure, multiply length by length by length:

Cube with all sides equal

Volume of a cube = length × length × length

Find the volume of a cube of length 20 cm.

Solution

Since the sides of a cube are equal, the volume of a cube is obtained by multiplying the length by length by length. That is,

Volume of a cube = length × length × length

= 20 cm × 20 cm × 20 cm

= 8,000 cm³

Therefore, the volume of the cube is 8,000 cm³