Solve density and mass problems

Home learning focus

Learn about density and mass and how to solve problems relating to them.

This lesson includes:

  • two videos
  • a learning summary
  • three activities with answers



Density describes how much space an object or substance takes up (ie its volume) in relation to the amount of matter the object or substance has in it (its mass).

To work out the density of an object or substance you can use this equation:

density = mass ÷ volume

The more dense a substance is, the heavier it feels for its size. If an object is heavy and compact, it has a high density.

Density in real-life situations

Watch this short case study video of a camera man explaining why density is an important factor when filming underwater.

The importance of density in underwater filming

Density values

The units used for density depend on the units used for mass and volume, but are usually: g/cm³ (if mass is measured in g and volume in cm³).

Here are the densities of some everyday substances:

  • Steel = 7.82 g/cm³

  • Water = 1.00 g/cm³

  • Air = 0.0013 g/cm³

These values show that the steel (solid) is the most dense while the air (gas) is the least dense.

The blue liquid in the jar is more dense than the yellow liquid, which is why they settle in separate layers.

Working out density

We now know that we can work out the density of an object if we know its mass and volume:

density = mass ÷ volume

Click through the slideshow below to see how you can work out the density of a chain by dividing its mass by its volume.

A ruler, a whiteboard, a calculator and some pens

Click to see a step-by-step slideshow.

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Density and mass problems

As you have learned, mass is the amount of matter that makes up an object or substance. If you know the density and volume of something, you can work out its mass with this equation:

mass = density × volume

Watch this video from Pearson to learn how to solve problems relating to density and mass, by working out the density of a new metal.

Find out the density of a new metal by working out the mass of its component parts


Activity 1

The density of a brooch

To get you thinking, have a go at this quick activity from BBC Bitesize, KS3 Maths to work out the density of a brooch when you know its mass and volume.

Activity 2

Interactive activity - practise finding density and mass

Now have a go at the questions in this interactive activity from MyMaths, Oxford University Press where you need to work through various problems to find density and mass. Click the 'Practice' button to enter. You can mark your answers within the activity.

Finding density and mass

Activity 3

Density and mass problems worksheet

Keep going - look at the problems relating to density and mass in this worksheet from Pearson, Maths Progress which test your skills in more depth. You will need a calculator to complete the questions. Write your answers on a piece of paper.

Solve density and mass problems

Click here to see the correct answers to the questions.

There's more to learn

Have a look at these other resources around the BBC and the web.

BBC Bitesize Daily
KS3 Maths
A Brief History of Mathematics
11-14 Maths
Bitesize Careers
Platinum Puzzle