Calculating the volume of cubes and cuboids

In a nutshell

The volume of a cube and cuboid can be calculated and compared. The volume can be measured in different units.

Cube

A cube is a 3D shape where all the faces are squares and the sides have the same length.

To work out the volume of a cube, find the length of one side then multiply it by itself twice. You can use the following formula to find the volume of a cube:

V=x^3

$V$	The Volume of the cube.
$x$	The length of a cube.

Example 1

Find the area of the cube.

Maths; Measurement; KS2 Year 6; Calculating the volume of cubes and cuboids

The length of one side is $2cm$ . Insert this value into the formula to work out the volume.

$Volume = x^3 \\Volume = 2^3 \\\underline{Volume = 8cm^3}$

Cuboid

A cuboid is a 3D shape where all the faces are rectangles and the parallel sides have the same length. The volume of a cuboid can be found using the following formula:

V=l \times w \times h

$V$	The Volume of the cuboid.
$l$	The length of the cuboid.
$w$	The width of the cuboid.
$h$	The height of the cuboid.

Example 2

Find the volume of the cuboid.

Maths; Measurement; KS2 Year 6; Calculating the volume of cubes and cuboids

$height = 2cm, \ width = 3cm, \ length = 4cm$

Substitute the values for height, width and length into the formula.

$Volume = l \times w \times h \\Volume = 4 \times 3 \times 2 \\\underline{Volume = 24cm^3}$

Units

The following units can be used to measure volume: $cm^3 \space \text{and} \space m^3$ for solids and $ml\ \text{and}\ l$ for liquids.