Question

An aluminium block has a volume of 480 cm3. What is the mass of the block if the density of aluminium is 2.7 g/cm3?

m=vx\rho

\rho=2.7 g/cm^3

v=480 cm^3

m = 480 cm3 x 2.7 g/cm3

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/cm3.

For larger volumes density is measured in kg/m3.

curriculum-key-fact
1 g/cm3 = 1 000 kg/m3
  • To convert from kg/m3 to g/cm3, divide by 1000.
  • To convert from g/cm3 to kg/m3, multiply by 1000.

Aluminium has a density of 2.7 g/cm3 = 2,700 kg/m3.

Water has a density of 1.0 g/cm3, or 1000 kg/m3.

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/m3?

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 m3

m = v \times \rho

\rho = 1000 kg/m3

v = 2500 m3

m = 2500 m3 x 1000 kg/m3

m = 2,500,000 kg

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