Density is a measure of how tightly the mass of an object is packed into the space it takes up. It can be calculated by dividing mass by volume .
Make sure you are happy with the following topics before continuing.
Density , mass and volume are all related by the formula,
where d is density , V is volume , and m is mass . This can be rearranged in order to find volume or mass depending on which quantities you are given and what the question asks you to find.
Mass is normally measured in grams, g, or kilograms, kg, whereas, volume is normally measured in cubic centimetres, cm ^3 , or cubic metres, m ^3 .
This means when dividing mass by volume, the resulting units are typically grams per cubic centimetre (g/cm ^3 ), or kilograms per cubic metre (kg/m ^3 ). These are compound units (for more information, see conversions revision).
Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC Cambridge iGCSE Edexcel iGCSEA handy way of remembering how to calculate either density , mass or volume is to use the triangles below.
The horizontal line means divide and the \times symbol means multiply.
We then cover up the one we want to find (represented by a red circle) and carry out the calculation with the other two values from the triangle.
Density Mass Volume Formula Pyramid" width="1964" height="427" />
Density Mass Volume Formula Pyramid" width="298" height="262" />
An object has a mass of 570 g and a volume of 2280 cm ^3 . Calculate its density .
[2 marks]
We’re looking for density, so constructing the triangle and covering d , we see we must divide the mass by the volume. So
Density Mass Volume Formula Pyramid" width="298" height="262" />
Density Mass Volume Formula Pyramid" width="298" height="262" />
A cat has volume 0.004 m ^3 and density 980 kg/m ^3 . Calculate the mass of the cat.
[2 marks]
We’re looking for mass, so constructing the triangle and covering m , we see that to calculate the mass we must multiply the density by the volume. So
\text < Mass >= 980 \times 0.004 = 3.92 kg
Density Mass Volume Formula Pyramid" width="298" height="262" />
Density Mass Volume Formula Pyramid" width="297" height="263" />
A bottle of water has a density of 1000 kg/m ^3 and mass of 0.5 kg. Calculate the volume of the water bottle giving your answer in litres.
[2 marks]
We’re looking for volume, so covering V , we must divide the mass by the density. So
Multiplying this by 1000 to convert into litres, gives us the final answer,
