10 AQA GCSE Physics questions on density (density = mass/volume, ρ = m/V) that get harder as you go, from Foundation to Higher, each with a full worked solution.
Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Equation sheet: given in the exam
📌 KEY DEFINITIONS – learn them word for word
Density is the mass per unit volume of a material. Unit: kg/m³.
Why a gas is much less dense than a solid: the particles in a gas are much further apart, so there is less mass in the same volume.
The equation
density = mass ÷ volume ρ = m / V
| Quantity | Symbol | Unit |
|---|---|---|
| density | ρ | kilograms per cubic metre (kg/m³) |
| mass | m | kilograms (kg) |
| volume | V | cubic metres (m³) |
Rearranged: m = ρ × V | V = m ÷ ρ | 1 cm³ = 1 × 10−6 m³; 1 litre = 0.001 m³; 1 g/cm³ = 1000 kg/m³
Use FIFA for every answer
- F – Formula: write the equation as it appears on the sheet.
- I – Insert: put in the numbers (convert to standard units first).
- F – Fix: rearrange to make the unknown the subject.
- A – Answer: calculate and always give the unit.
Foundation: aim for Q1–8. Higher: aim for Q4–10. Most questions need rearranging.
Questions
Q1 (F) A block of plastic has a mass of 2 kg and a volume of 0.001 m³. Calculate its density.
Show solution
F: ρ = m / V
I: ρ = 2 ÷ 0.001
F: ρ is already the subject
A: 2000 kg/m³
Q2 (F) A bath holds 0.2 m³ of water (ρ = 1000 kg/m³). Calculate the mass of the water.
Show solution
F: ρ = m / V
I: 1000 = m ÷ 0.2
F: m = 1000 × 0.2
A: 200 kg
Q3 (F) A 540 kg batch of aluminium (ρ = 2700 kg/m³) arrives at a factory. Calculate its volume.
Show solution
F: ρ = m / V
I: 2700 = 540 ÷ V
F: V = 540 ÷ 2700
A: 0.2 m³
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Q4 (F) A gold ring has a mass of 19.3 g and a volume of 1.0 cm³. Calculate its density in kg/m³.
Show solution
Convert first: 19.3 g = 0.0193 kg; 1.0 cm³ = 1.0 × 10−6 m³
F: ρ = m / V
I: ρ = 0.0193 ÷ 1.0 × 10−6
F: ρ is already the subject
A: 19 300 kg/m³
Q5 (F) Olive oil has a density of 920 kg/m³. Calculate the mass of a 1.5 litre bottle of oil.
Show solution
Convert first: 1.5 litres = 0.0015 m³
F: ρ = m / V
I: 920 = m ÷ 0.0015
F: m = 920 × 0.0015
A: 1.38 kg
Q6 (F/H) A 260 g stone is lowered into a measuring cylinder. The water level rises from 50 cm³ to 150 cm³. Calculate the density of the stone in kg/m³.
Show solution
Volume of stone: 150 − 50 = 100 cm³ = 1.0 × 10−4 m³; mass = 0.26 kg
F: ρ = m / V
I: ρ = 0.26 ÷ 1.0 × 10−4
F: ρ is already the subject
A: 2600 kg/m³
Q7 (F/H) A bedroom is 5 m long, 4 m wide and 2.5 m high. Air has a density of 1.2 kg/m³. Calculate the mass of air in the room.
Show solution
Volume: 5 × 4 × 2.5 = 50 m³
F: ρ = m / V
I: 1.2 = m ÷ 50
F: m = 1.2 × 50
A: 60 kg
Q8 (F/H) The Earth has an average density of 5.5 × 103 kg/m³ and a volume of 1.1 × 1021 m³. Calculate its mass, to 2 significant figures.
Show solution
F: ρ = m / V
I: 5.5 × 103 = m ÷ 1.1 × 1021
F: m = 5.5 × 103 × 1.1 × 1021 = 6.05 × 1024 kg
A: 6.1 × 1024 kg (2 s.f.)
Q9 (H) A block of ice has a volume of 0.50 m³. Ice has a density of 920 kg/m³. Calculate the weight of the block. (g = 9.8 N/kg)
Show solution
Step 1 – mass
F: ρ = m / V
I: 920 = m ÷ 0.50
F: m = 920 × 0.50 = 460 kg
Step 2 – weight
W = m g = 460 × 9.8
A: 4508 N
Q10 (H) A metal cube has sides of 4.0 cm and a mass of 170 g. Calculate its density in kg/m³, to 2 significant figures.
Show solution
Volume: 4.0 × 4.0 × 4.0 = 64 cm³ = 6.4 × 10−5 m³; mass = 0.170 kg
F: ρ = m / V
I: ρ = 0.170 ÷ 6.4 × 10−5
F: ρ = 2656 kg/m³
A: 2700 kg/m³ (2 s.f.)
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