Calculating volume

Volume is a measure of space taken up by a 3-dimensional shape and is measured in \(mm^{3}\), \(cm^{3}\) etc.

Volume can also be measured in litres with \(1\, litre = 1000\,cm^{3}\).

Make sure you don't confuse volume (for 3-D shapes) and area (for 2-D shapes).

Converting units

To convert litres to \(cm^{3}\), we multiply by \(1\,000\).

\[5\; litres = 5 \times 1\,000 = 5\,000cm^{3}\]

\(23.6\; litres = 23.6 \times 1000 = 23\,600cm^{3}\)3

To convert \(cm^{3}\) to litres, we divide by \(1\,000\).

\[8\,000cm^{3} = 8\; litres\]

\[125\, 000cm^{3} = 125\; litres\]

\[7\,530cm^{3} = 7.53\; litres\]


Sam is going to buy some cola for her son’s birthday party. The cola comes in one-litre bottles. The plastic cups she has each hold about 90 millilitres. 14 children have been invited and Sam reckons about 3 cups each would be appropriate over the afternoon.

How many one-litre bottles should she buy?

\[Amount\,for\,1\,child = 90 \times 3 = 270ml\]

\[Amount\,for\,14\,children = 270 \times 14 =3\,780\,ml\]

One litre is \(1\,000\,ml\) so Sam needs to buy \(4\) one-litre bottles.