IGCSE Maths / Direct and inverse proportion

Density, mass and volume revision notes

Edexcel International GCSE Maths (4MA1), chapter 21: Direct and inverse proportion, specification point 4.4g. Free lesson.

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Density is mass divided by volume, and you can rearrange the formula to find mass. Match the mass and volume units to the density unit before calculating.

What density measures

Density tells you how much mass is packed into a given volume. It is a compound measure because its unit combines two units, such as grams per cubic centimetre. Density = mass ÷ volume D = M/V D is density, M is mass and V is volume. For density in g/cm³, use mass in grams and volume in cm³.

How to find density

Use D = M/V, but check the units before dividing. Convert the mass or volume first if its unit does not match the density unit required.

How to find mass

Rearrange D = M/V to make mass the subject. Multiply both sides by V, so the V dividing M cancels. This gives M = DV. This formula is not on the formula sheet, so learn it. The units multiply too: g/cm³ × cm³ leaves g. This is a useful check that the formula is the right way round.

How to convert g/cm³ to kg/m³

Convert the mass unit first, then the volume unit. Since 1000 g = 1 kg, divide the density value by 1000. Since 1 m = 100 cm, 1 m³ = 100 × 100 × 100 = 10⁶ cm³, so multiply by 10⁶ for the volume step. The two changes combine to multiplying the original value by 1000. So 1 g/cm³ = 1000 kg/m³. Water has the same density written as 1 g/cm³ or 1000 kg/m³.

Check units before calculating

The unit asked for in the answer tells you which units to use in the formula. Convert before substituting, and write the converted value on its own line so the unit conversion is clear. For g/cm³, use grams and cm³. A cubic metre is a million cubic centimetres, not 100 cm³.