Density, mass and volume GCSE Questions and Worked Answers

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Start with the meaning

What you need to know about density, mass and volume

Imagine two blocks that take up exactly the same amount of space. One has a mass of 20 g and the other 80 g. The second contains more mass in that same volume, so it is denser. Density compares mass with space, rather than comparing mass alone.

See the idea first

‘Grams per cubic centimetre’ tells you the comparison

Volume measures space in cubic units. A density of 3 g/cm³ means each 1 cm³ of a uniform material has mass 3 g. Write m for mass, V for volume and ρ (rho) for density. Then m = ρV, so ρ = m ÷ V and V = m ÷ ρ.

One material of density 3 g/cm³
Volume (cm³)	Mass (g)	Mass ÷ volume
1	3	3
4	12	3
10	30	3

From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Find density

What the problem asks: A sample has mass 72 g and volume 24 cm³. Find its density.

How to solve it: 72 ÷ 24 = 3 g/cm³. The calculation finds the mass belonging to one cubic centimetre.

Find mass

What the problem asks: A uniform material has density 2.5 g/cm³ and volume 40 cm³. Find its mass.

How to solve it: There are 40 groups of 2.5 g: mass = 2.5 × 40 = 100 g.

Combine materials

What the problem asks: Mix samples with masses 80 g and 120 g and volumes 20 cm³ and 60 cm³. Assume volumes add. Find density.

How to solve it: Total mass is 200 g, total volume is 80 cm³. Divide: 200 ÷ 80 = 2.5 g/cm³. Do not simply average the two densities.

A reliable routine

Use a mass-per-volume relationship

Use this for a uniform substance, or for average density of a whole sample. The formula is a unitary calculation: total mass divided into equal units of volume. Mixtures require totals and an explicit assumption about the final volume.

Identify which of mass, density or volume is missing.
Convert mass and volume into units matching the density.
Use m = ρV, ρ = m ÷ V or V = m ÷ ρ.
For a combined sample, total the masses and use its actual or assumed total volume before dividing.

Check: 1 m³ = 100 × 100 × 100 = 1,000,000 cm³. Cubic units do not convert with a single factor of 100.

Fully worked

Density, mass and volume GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Find density

2 marks

Question

A block has mass 156 g and volume 60 cm³. Find its density.

\rho=\frac{156}{60}=2.6\text{ g/cm}^3

This is 2.6 g for each cubic centimetre.

Example 2

Find mass

2 marks

Question

A material has density 7.2 g/cm³. Find the mass of 25 cm³.

m=7.2\times25=180\text{ g}

Multiply the mass of one cm³ by the number of cm³.

Example 3

Find volume

2 marks

Question

A sample has mass 315 g and density 9 g/cm³. Find its volume.

V=\frac{315}{9}=35\text{ cm}^3

There are 35 lots of 9 g.

Example 4

Volume first, then density

3 marks

Question

A cuboid is 5 cm by 4 cm by 3 cm and has mass 162 g. Find its density.

First find space occupied.

V=5\times4\times3=60\text{ cm}^3

\rho=162/60=2.7\text{ g/cm}^3

Tip: use volume, not the surface area.

Example 5

Convert density units

3 marks

Question

Convert 1.2 g/cm³ to kg/m³.

One cubic metre contains 1,000,000 cm³. Its mass is

1.2\times1000000=1200000\text{ g}

1200000/1000=1200\text{ kg}

Density is 1200 kg/m³.

Example 6

A mixture

Harder4 marks

Question

Combine 30 cm³ of material at 4 g/cm³ with 50 cm³ at 2 g/cm³. Assume no material is lost and volumes add. Find the mixture density.

Masses are $30\times4=120$ g and $50\times2=100$ g.

m_{\rm total}=220\text{ g}

V_{\rm total}=80\text{ cm}^3

\rho=220/80=2.75\text{ g/cm}^3

A simple average of 4 and 2 would ignore the unequal volumes.

10 original questions · total 26 marks

Density, mass and volume GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 31 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed

1

Density

2 marks

A 48 cm³ sample has mass 144 g. Find density.

Show worked answer

\rho=144/48=3\text{ g/cm}^3

Divide by the volume to find mass per cm³.

2

Mass

2 marks

Find mass for density 0.8 g/cm³ and volume 75 cm³.

Show worked answer

m=0.8\times75=60\text{ g}

3

Volume

2 marks

Find volume for mass 560 g and density 7 g/cm³.

Show worked answer

V=560/7=80\text{ cm}^3

4

Kilograms to grams

3 marks

A block has mass 1.5 kg and volume 500 cm³. Find density in g/cm³.

Show worked answer

1.5\text{ kg}=1500\text{ g}

\rho=1500/500=3\text{ g/cm}^3

5

A cylinder

3 marks

A cylinder has radius 2 cm, height 5 cm and mass $60\pi$ g. Find its density.

Show worked answer

V=\pi(2)^2(5)=20\pi\text{ cm}^3

\rho=\frac{60\pi}{20\pi}=3\text{ g/cm}^3

Keep π exact so it cancels.

6

Compare

3 marks

A has mass 100 g and volume 40 cm³. B has mass 90 g and volume 30 cm³. Which is denser?

Show worked answer

A: $100/40=2.5$ g/cm³. B: $90/30=3$ g/cm³. B is denser despite having less total mass.

7

Cubic conversion

2 marks

Convert 2500 kg/m³ to g/cm³.

Show worked answer

One m³ has mass 2,500,000 g and volume 1,000,000 cm³.

\rho=2500000/1000000=2.5\text{ g/cm}^3

8

Combined density

4 marks

Two samples have masses 45 g and 75 g and volumes 15 cm³ and 25 cm³. Assuming volumes add, find combined density.

Show worked answer

m=45+75=120\text{ g}

V=15+25=40\text{ cm}^3

\rho=120/40=3\text{ g/cm}^3

Both components already have this density.

9

Water displacement

3 marks

A solid is fully submerged in a measuring cylinder. Water rises from 35 cm³ to 59 cm³. Its mass is 192 g. Find its density.

Show worked answer

The displaced volume is

59-35=24\text{ cm}^3

\rho=192/24=8\text{ g/cm}^3

Use the rise, not the final reading.

10

A modelling assumption

2 marks

Why might adding the separate liquid volumes give the wrong density after mixing?

Show worked answer

Some liquids change total volume on mixing. Total mass divided by an incorrect volume gives an incorrect density. Use the measured final volume unless the problem tells you volumes add.

Examiner-style feedback

Common density, mass and volume mistakes

Judging density by mass alone

Compare mass per equal volume, not just which object is heavier.

Confusing surface area with volume

Density divides mass by occupied space in cubic units.

Averaging component densities

Use total mass ÷ total volume; an unweighted mean need not work.

30-second recap

Choose, carry out, check

Translate the wording before you reach for a rule.

Read the compound units.
Find the actual volume.
Use mass = density × volume.
Combine totals before finding a mixture density.

Quick answers

Density, mass and volume FAQ

Can two different-size objects have the same density?

Yes. If they are made of the same uniform material, mass grows in proportion to volume.

Is density always in g/cm³?

No. kg/m³ is also common. Match the mass and volume units to the requested answer.

Build connected skills

What to revise next

Find the space occupied

Volume

Calculate cuboid, prism and cylinder volumes.

Revise volume

Another compound rate

Speed, distance and time

Compare a distance with its time.

Revise speed, distance and time

Content standards

Curriculum and rights review

R1/R11 density and compound units across tiers; original multi-step mixtures marked harder, not blanket Higher. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.

Official specification references

AQA GCSE Maths subject content