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Density

FoundationHigherAQAEdexcelOCR

Get to grips with density using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on density, mass and volume calculations, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Density = mass ÷ volume.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Density is the mass of a substance per unit of volume, calculated as \(\text{density} = \frac{\text{mass}}{\text{volume}}\).

It explains why a small piece of lead feels heavier than a much larger piece of polystyrene. Common units are grams per cubic centimetre or kilograms per cubic metre.

The formula rearranges to give mass or volume when the other two are known. A formula triangle helps, but understanding that density is mass divided by volume is more reliable, since it lets you rearrange from first principles rather than remembering a picture.

Revision notes

The formula

\(\rho = \frac{m}{V}\), where \(\rho\) is density, \(m\) is mass and \(V\) is volume.

A block of mass \(240\)g and volume \(30\)cm³ has density \(240 \div 30 = 8\)g/cm³.

Rearranging

Mass equals density times volume, and volume equals mass divided by density.

So a substance of density \(2.5\)g/cm³ occupying \(40\)cm³ has mass \(100\)g.

Units and consistency

The units of density come from the units of mass and volume, such as g/cm³ or kg/m³.

Everything must be in consistent units before calculating, so convert first if mass is in kilograms and volume in cubic centimetres.

Key points

  • Density is mass divided by volume.
  • Mass equals density times volume.
  • Volume equals mass divided by density.
  • Common units are g/cm³ and kg/m³.
  • Convert to consistent units before calculating.
  • Denser materials have more mass per unit volume.

Worked examples

Example 1

A block has mass \(450\)g and volume \(50\)cm³. Find its density.

Working

\[\frac{450}{50}\]divide mass by volume
\[= 9\text{g/cm}^3\]state the density with units

Example 2

A substance has density \(3\)g/cm³ and volume \(25\)cm³. Find its mass.

Working

\[m = \rho V = 3 \times 25\]mass equals density times volume
\[= 75\text{g}\]state the mass

Example 3

A metal of density \(8\)g/cm³ has mass \(200\)g. Find its volume.

Working

\[V = \frac{m}{\rho} = \frac{200}{8}\]volume equals mass divided by density
\[= 25\text{cm}^3\]state the volume

Common mistakes

  • Multiplying instead of dividing.

    Density is mass divided by volume, not the product.

  • Mixing units.

    Convert kilograms to grams, or cubic metres to cubic centimetres, before calculating.

  • Omitting the units.

    Density units combine mass and volume units, such as g/cm³.

  • Confusing density with mass.

    A dense material is not necessarily heavy — it depends on how much of it there is.

Exam tips

  • Write the formula before substituting.
  • Check the units match before calculating.
  • Include compound units in the answer.
  • Rearrange from the formula rather than relying on a triangle.

Key terms

Density
Mass per unit volume.
Mass
The amount of matter in an object.
Volume
The space an object occupies.
Compound unit
A unit combining two others, such as g/cm³.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.