Density of Materials
Revise Density of Materials for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Density is the mass per unit volume, calculated using ρ = m/V, and depends on how closely packed the particles are.
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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.
Topic overview
Density is the mass per unit volume of a substance. The equation is density = mass ÷ volume, with mass in kilograms, volume in cubic metres, and density in kilograms per cubic metre. This is a required practical.
The density of a material depends on how closely its particles are packed. Solids are usually densest because their particles are closely packed in a regular arrangement. Gases are least dense because their particles are far apart.
To find the density of an irregular solid, measure its mass on a balance and find its volume using a displacement can — the volume of water displaced equals the volume of the object. For a regular solid, measure the dimensions and calculate the volume.
Revision notes
The equation
Density = mass ÷ volume, ρ = m ÷ V.
Mass in kilograms, volume in cubic metres, density in kg/m³. It can also be given in g/cm³, and 1 g/cm³ equals 1000 kg/m³.
Density and particle arrangement
Solids are usually densest, because their particles are closely packed in a regular arrangement.
Liquids are slightly less dense, with particles close but randomly arranged. Gases are far less dense, because the particles are widely spaced.
Measuring density
Regular solid: measure the dimensions with a ruler and calculate the volume, then measure the mass on a balance.
Irregular solid: measure the mass, then lower it into a displacement can and collect the water that overflows. The volume of water displaced equals the volume of the object.
Key points
- Density = mass ÷ volume.
- Density is measured in kg/m³ or g/cm³.
- Solids are usually densest.
- Gases are least dense because particles are far apart.
- A displacement can finds the volume of an irregular solid.
- The water displaced equals the object's volume.
Worked examples
Example 1
A block has a mass of 240 g and a volume of 80 cm³. Calculate its density. [2 marks]
Model answer
Density = mass ÷ volume = 240 ÷ 80 (1 mark) = 3 g/cm³ (1 mark).
Example 2
Describe how you would find the volume of an irregularly shaped stone. [3 marks]
Model answer
Fill a displacement can until water runs from the spout and stops (1 mark). Lower the stone gently into the can and collect the water that overflows in a measuring cylinder (1 mark). The volume of water collected equals the volume of the stone (1 mark).
Example 3
Explain why gases have much lower densities than solids. [2 marks]
Model answer
In a gas the particles are far apart with large spaces between them (1 mark), so there is much less mass in the same volume than in a solid where particles are closely packed (1 mark).
Common mistakes
Dividing volume by mass.
Density is mass ÷ volume, not the other way round.
Mixing units.
Use kg and m³ together, or g and cm³ together — never a mixture.
Measuring the volume of water before immersion.
It is the water DISPLACED that gives the volume, so collect the overflow.
Saying gases have no density.
They have a low density, not zero.
Exam tips
- Write the equation before substituting.
- Keep the units consistent throughout.
- Describe the displacement method as a clear sequence.
- Explain density differences through particle spacing.
Key terms
- Density
- Mass per unit volume.
- Displacement can
- Apparatus for finding the volume of an irregular solid.
- Volume
- The space occupied, in m³ or cm³.
- Particle arrangement
- How closely particles are packed together.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.