Year 7 Interactive Maths - Second Edition

Volume of a Solid

If the rectangular box were filled with 1 cm cubes, there would be:

6 × 2 cubes in the bottom layer

As there are 3 layers,

Now note that the area of the box's base is given by:

From the above discussion, we can derive a formula for the volume of a rectangular box as follows:

In general:

The volume, V, of a solid is given by

where A is the area of the base (or cross-section) of the solid and h is the height.

The volume of the following solids are often required to solve real world problems.

A cube of side-length l units has a volume of V cubic units given by

A cuboid with length l units, width w units and height h units has a volume of V cubic units given by

Example 2

Find the volume of a cube of side 10 cm.

Solution:

Example 3

Find the volume of a brick 20 cm by 10 cm by 5 cm.

Solution:

Key Terms

solid, volume formula, base, height, volume of a cube, volume of a cuboid