Density – Intermediate and Higher tier - Compound measures - WJEC - GCSE Maths Numeracy (WJEC) Revision

Density – Intermediate and Higher tier

Density is a measure of how much mass an object has per unit volume. Density is a compound measure because mass and volume can’t be measured in the same units.

A tank of water with one soft drinks can at the bottom and another floating on the surface — Figure caption,
Objects denser than water sink, while less dense objects float. An interesting example of this can be found with cans of normal and sugar-free soft drink

Mass is a measure of how much matter is in an object, and is usually measured in kilograms (kg). Weight is the force that same amount of matter would push down on the Earth with, and is measured in Newton (N).

This is difficult to come to terms with because the two terms are often used incorrectly in everyday life. Your weighing scale may tell you that you weigh 88 kg. However, this is your mass - your weight would actually be about 880 N.

The equation for density is:

\(\text{density}=\frac{\text{mass}}{\text{volume}}\)

This equation can also be rearranged to:

\(\text{mass}=\text{density}\times{\text{volume}}\)

and

\(\text{volume}=\frac{\text{mass}}{\text{density}}\)

Density is commonly measured in either kg/m³ or g/cm³.

Compound measures mass, density and volume — Figure caption,
An equation triangle is a tool that can be used to help rearrange equations

Question

Aluminium is a very low density metal so it is used to build all sorts of vehicles.

Calculate the density of aluminium if 20 cm³ has a mass of 54 g.

Question

Gold is expensive and desirable not only because of its colour and shine but also because it does not rust easily. Jimmy wants to build a sports car made of gold but is worried about the mass. The density of gold is 19,300 kg/m³ and the average sports car has a volume of roughly 1.5 m³.

Calculate the mass of a golden sports car.

Compound measures - WJECDensity – Intermediate and Higher tier