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:

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Example 1

Find the area of the cube.

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:

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Example 2

Find the volume of the cuboid.

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

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

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