Speed and Density
Speed and density are compound measures that combine two other quantities: speed is calculated as distance divided by time, and density is calculated as mass divided by volume. Both use a formula triangle for rearranging, and they appear throughout GCSE calculator and ratio questions involving units such as km/h, m/s and g/cm^3.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the two key formulae: speed = distance / time, and density = mass / volume.
- Use a formula triangle (or rearrange algebraically) to find whichever quantity is missing: cover the one you want to find, and the triangle shows whether to multiply or divide the other two.
- Make sure all quantities are in consistent units before calculating; convert times to hours or seconds, and lengths or masses to matching units, as needed.
- Substitute the known values into the correct version of the formula and calculate.
- Check the units of your answer match the units asked for in the question, converting again if necessary.
- For problems involving mixtures or multiple stages, work out each part's mass or distance separately before combining them for an overall density or average speed.
Worked example
A block of copper has a mass of 356 g and a volume of 40 cm^3. Work out the density of the copper, in g/cm^3.
- Recall the formula: density = mass / volume.
- Substitute the values: density = 356 / 40.
- Work out the calculation: density = 8.9.
- State the final answer, with units: the density of the copper is 8.9 g/cm^3.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
The density of silver is 10.5 g/cm^3. A silver bar has a mass of 315 g. Work out the volume of the bar.
Priya drives 108 km in 1 hour 24 minutes. She then drives a further 72 km in 36 minutes. Work out her average speed for the whole journey. Give your answer in km/h.
An alloy is made by combining 50 cm^3 of copper, density 8.9 g/cm^3, with 30 cm^3 of zinc, density 7.1 g/cm^3. Work out the density of the alloy. Give your answer correct to 3 significant figures.
See real past-paper questions on speed and density, organised by topic with official mark schemes →
Free printable worksheet
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