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 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.
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.
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.
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.
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.
There's more to learn
Have a look at these other resources around the BBC and the web.