Volume of prisms

A right rectangular prism is a solid in which:

• the base is a rectangle
• its horizontal plane cross-sections are rectangles congruent to the base
• all six faces are rectangles

(We usually leave out the word 'right' which simply indicates that the 'walls are vertical'.)

If all the faces of the prism are squares then the rectangular prism is a cube.

The volume of a rectangular prism is a measure of the space inside the prism.

Suppose the side lengths of the prism are 5 m, 4 m and 3 m, as in the diagram. We can cut the rectangular prism up into 1-cubic-metre cubes. Altogether there are 5 × 4 × 3 = 60 cubes. We define the volume of each cube to be 1 cubic metre, and then the volume of the rectangular prism is 60 cubic metres, or 60 m³. The side lengths of the rectangular prism are generally called the length, the width and the height, and so the volume of a rectangular prism is given by:

Volume of a rectangular prism = length × width × height = lwh