Density is used to make a fair comparison between materials.

- Question
An aluminium block has a volume of 480 cm

^{3}. What is the mass of the block if the density of aluminium is 2.7 g/cm^{3}?m = 480 cm

^{3}x 2.7 g/cm^{3}m = 1296 g

The mass of the aluminium block is 1 296 g or 1.296 kg.

**The units of density**

For small volumes density is measured in g/cm^{3}.

For larger volumes density is measured in kg/m^{3}.

1 g/cm^{3} = 1 000 kg/m^{3}

- To convert from kg/m
^{3}to g/cm^{3}, divide by 1000. - To convert from g/cm
^{3}to kg/m^{3}, multiply by 1000.

Aluminium has a density of 2.7 g/cm^{3} = 2,700 kg/m^{3}.

Water has a density of 1.0 g/cm^{3}, or 1000 kg/m^{3}.

Knowing the density of a material enables an engineer or architect to calculate the mass of a building or structure from its volume.

This in turn enables them to determine the correct depth of foundation to make the building safe.

- Question
An Olympic size swimming pool measures 50 m long, 25 m wide and has an average depth 2 m. What is the mass of water in the pool if the density of water is 1000 kg/m

^{3}?The swimming pool is a regular shape and so the volume of water is calculated using the equation:

Volume = length x breadth x height

Volume = 50 m x 25 m x 2 m = 2500 m

^{3}m =

1000 kg/m

^{3}v = 2500 m

^{3}m = 2500 m

^{3}x 1000 kg/m^{3}m = 2,500,000 kg

The mass of water in the swimming pool is 2,500,000 kg or 2500 tonnes.