Density (AQA GCSE Maths): Revision Notes

Density

What is density?

Density is a measure of how much mass is packed into a given volume. It tells us how tightly matter is squeezed together in a material. The formal definition states that density is the mass per unit volume of a material.

Different materials have different densities. For example, lead has a much higher density than wood because the same volume of lead contains much more mass than the same volume of wood.

The density formula

The relationship between mass, density, and volume can be remembered using a formula triangle. This triangle helps you rearrange the formula depending on what you need to find.

The three key relationships are:

• $\text{Density} = \frac{\text{mass}}{\text{volume}}$
• $\text{Volume} = \frac{\text{mass}}{\text{density}}$
• $\text{Mass} = \text{density} \times \text{volume}$

Units for density

Density is measured using two main units:

• Grammes per cubic centimetre (g/cm³) - commonly used for smaller objects and materials
• Kilogrammes per cubic metre (kg/m³) - commonly used for larger objects and in scientific contexts

Calculating with density

Finding mass from density and volume

When you know the density and volume of an object, you can calculate its mass using:

$\text{Mass} = \text{density} \times \text{volume}$

First, work out the volume if it's not given directly. For prisms, the volume equals the cross-sectional area multiplied by the length.

Finding density from mass and volume

When you know both the mass and volume, you can calculate density using:

$\text{Density} = \frac{\text{mass}}{\text{volume}}$

Remember to use consistent units throughout your calculation.

Problem-solving approach

When tackling density problems, follow this systematic approach:

Exam tips

Remember!