Compound measures

Objective. Reason with density, pressure and population density.

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Learn: the key idea

Compound measures combine two quantities into one rate, such as density (mass÷volume), pressure (force÷area), or population density (population÷area). To find density, divide mass by volume: a block of mass 50g and volume 10cm³ has density 50÷10=5g/cm³. These formulas can be rearranged to find any of the three quantities: mass=density×volume, or volume=mass÷density. Units must match the formula, so always convert measurements to consistent units, such as cm³ for volume and g for mass, before calculating. Checking the resulting units (such as g/cm³ for density) confirms the calculation makes physical sense.

Worked example

A metal block has a mass of 316 g and a volume of 40 cm³. Calculate its density.

1 $Density formula: density = mass \div volume$
2 $Substitute values: density = 316 \div 40$
3 $Calculate: 316 \div 40 = 7.9$
4 $State with units: density = 7.9 g/cm³$

Answer: 7.9 g/cm³

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Common mistake. Pupils divide the quantities the wrong way round, computing volume÷mass instead of mass÷volume for density. For mass=50g and volume=10cm³, this wrongly gives 0.2 instead of 5g/cm³. Always match the formula structure (mass over volume) exactly before dividing.

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