IGCSE Physics 0625 · Topic 1.4

IGCSE Physics Density Questions and Worked Solutions

50 topic-wise practice questions on Density (Unit 1: Motion, Forces and Energy), written to the Cambridge IGCSE Physics 0625 syllabus for 2026–2028, each with a step-by-step worked solution.

50 questions30 Core10 Extended10 Challenge123 marksTextbook §1.4 · pp. 29–32

Questions tagged Core are for all candidates (Papers 1 & 3). Questions tagged Extended are Supplement content (Papers 2 & 4). Questions 41–50 are harder Challenge questions. Try each question first, then tap Show solution to check your working.

Topic guide: Density

Density tells you how much mass is packed into a given volume. It explains why some objects float and others sink, and it can identify materials. You must know how to measure the density of regular solids, irregular solids and liquids.

Key formulas

ρ = m ÷ V	density ρ (kg/m³ or g/cm³), mass m, volume V	Core
V = l × w × h	volume of a cuboid	Core
V = V₂ − V₁	volume of an irregular object by displacement	Core
1 g/cm³ = 1000 kg/m³	unit conversion	Core

Prerequisite knowledge

Mass (1.3) and measuring volume (1.1)
Volume of a cuboid
Unit conversion between g, kg, cm³ and m³

Exam tips & common mistakes

Keep units consistent: g with cm³ gives g/cm³; kg with m³ gives kg/m³
Water has density 1.0 g/cm³ (1000 kg/m³) — useful for float/sink questions
When describing displacement, mention reading the meniscus at eye level

Key facts from the syllabus (1.4)

Regular solid: measure mass with a balance and calculate volume from dimensions
Irregular solid: find volume by displacement (measuring cylinder or displacement can)
Liquid: find the mass of a known volume by weighing the container empty and full
An object floats in a liquid if its density is less than the liquid's density
Extended liquids that do not mix form layers with the least dense on top
Density is a property of the material, not the size of the sample

Textbook: §1.4 Density, pp. 29–32

Core[1 mark]

Define density.

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Method: ρ = m/V.

Mass per unit volume

Core[2 marks]

A block has mass 540 g and volume 200 cm³. Calculate its density.

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Method: ρ = m ÷ V.

ρ = 540 ÷ 200 = 2.70 g/cm³

Core[3 marks]

A rectangular block measures 4.0 cm × 3.0 cm × 2.5 cm and has a mass of 237 g. Calculate its density.

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Method: V = l × w × h.

V = 30.0 cm³; ρ = 237 ÷ 30 = 7.90 g/cm³

Core[2 marks]

Calculate the mass of 250 cm³ of oil of density 0.92 g/cm³.

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Method: m = ρV.

m = 0.92 × 250 = 230 g

Core[2 marks]

Calculate the volume of 1350 g of aluminium (density 2.7 g/cm³).

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Method: V = m ÷ ρ.

V = 1350 ÷ 2.7 = 500 cm³

Core[4 marks]

Describe how to find the density of an irregularly shaped stone that sinks in water.

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Method: Mass from a balance; volume by displacement in a measuring cylinder; then divide.

Measure mass on a balance; read water level V₁, lower stone in, read V₂; volume = V₂ − V₁; density = mass ÷ volume

Core[3 marks]

Describe how to measure the density of a liquid.

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Method: Find mass of liquid by difference; read volume in a measuring cylinder.

Weigh an empty measuring cylinder, add liquid and read the volume, weigh again; mass = difference; ρ = m ÷ V

Core[3 marks]

An empty measuring cylinder has mass 120 g. With 80 cm³ of liquid it has mass 216 g. Calculate the density of the liquid.

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Method: Mass of liquid = 216 − 120.

m = 96 g; ρ = 96 ÷ 80 = 1.20 g/cm³

Core[2 marks]

A stone of mass 156 g raises a water level from 50 cm³ to 70 cm³. Calculate the density of the stone.

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Method: V = 20 cm³.

ρ = 156 ÷ 20 = 7.80 g/cm³

Core[1 mark]

Water has a density of 1.0 g/cm³. A wooden block has density 0.65 g/cm³. State whether it floats or sinks in water.

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Method: Objects less dense than the liquid float.

It floats (0.65 < 1.0)

Core[1 mark]

A metal object has density 7.9 g/cm³. State whether it floats in mercury (13.6 g/cm³).

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Method: Compare densities.

It floats (7.9 < 13.6)

Core[2 marks]

Convert a density of 2.7 g/cm³ into kg/m³.

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Method: 1 g/cm³ = 1000 kg/m³.

2.7 × 1000 = 2700 kg/m³

Core[3 marks]

A cube of side 2.0 cm has a mass of 71.2 g. Calculate its density and suggest the material (copper 8.9 g/cm³, iron 7.9 g/cm³).

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Method: V = 2.0³ = 8.0 cm³.

ρ = 71.2 ÷ 8.0 = 8.90 g/cm³; copper

Core[2 marks]

A ball of mass 0.050 kg has a volume of 6.0 × 10⁻⁵ m³. Calculate its density in kg/m³.

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Method: ρ = m ÷ V.

ρ = 0.050 ÷ 6.0×10⁻⁵ = 833 kg/m³

Core[2 marks]

An object sinks in water (1.00 g/cm³) and in oil (0.85 g/cm³) but floats in mercury (13.6 g/cm³). State the range of its density.

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Method: It is denser than water but less dense than mercury.

Between 1.00 g/cm³ and 13.6 g/cm³

Core[2 marks]

Calculate the density of a 3000 kg block of concrete with volume 1.25 m³.

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Method: ρ = m ÷ V.

ρ = 3000 ÷ 1.25 = 2400 kg/m³

Core[2 marks]

Calculate the mass of air in a room of volume 60 m³ (density of air 1.2 kg/m³).

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Method: m = ρV.

m = 1.2 × 60 = 72.0 kg

Core[2 marks]

Gold has density 19.3 g/cm³. Calculate the mass of a gold bar of volume 50 cm³.

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Method: m = ρV.

m = 19.3 × 50 = 965 g

Core[2 marks]

Calculate the volume of 500 g of mercury (density 13.6 g/cm³).

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Method: V = m ÷ ρ.

V = 500 ÷ 13.6 = 36.8 cm³

Core[3 marks]

A cylinder has radius 2.0 cm and height 10 cm. Its mass is 340 g. Calculate its density.

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Method: V = πr²h.

V = π × 2.0² × 10 = 126 cm³; ρ = 340 ÷ 126 = 2.71 g/cm³

Core[2 marks]

Explain why a large block of polystyrene can have less mass than a small block of iron.

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Method: Density.

Polystyrene has a much lower density than iron, so even a large volume has a small mass

Core[2 marks]

A 20 cm³ piece of wood has mass 12 g. State whether it floats in water (1.0 g/cm³), explaining your answer.

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Method: Compare densities.

ρ = 12 ÷ 20 = 0.600 g/cm³, less than water, so it floats

Core[3 marks]

A 100 g block is placed in a full displacement can and 37 cm³ of water overflows into a measuring cylinder. Calculate the density of the block.

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Method: Volume = overflow.

ρ = 100 ÷ 37 = 2.70 g/cm³

Core[2 marks]

State why a displacement (Eureka) can is useful for measuring the volume of a large irregular object.

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Method: Object doesn't fit in cylinder.

The object may be too large for a measuring cylinder; the overflow water collected equals its volume

Core[2 marks]

An empty beaker has mass 85 g. With 150 cm³ of salt solution it has mass 262 g. Calculate the density of the solution.

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Method: Mass by difference.

ρ = (262 − 85) ÷ 150 = 1.18 g/cm³

Core[2 marks]

A metal block has dimensions 2.0 cm × 5.0 cm × 10 cm and density 7.9 g/cm³. Calculate its mass.

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Method: m = ρV.

V = 100 cm³; m = 7.9 × 100 = 790 g

Core[2 marks]

A sample of a liquid has density 0.80 g/cm³. Calculate the mass of 2.0 litres of it in kg.

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Method: 1 L = 1000 cm³.

m = 0.80 × 2000 = 1600 g = 1.60 kg

Core[1 mark]

State what happens to the density of a piece of metal if it is cut in half.

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Method: Intrinsic property.

It stays the same

Core[3 marks]

Two blocks A and B have equal mass. A has volume 25 cm³ and B has volume 75 cm³. Find the ratio of their densities.

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Method: ρ ∝ 1/V for equal mass.

ρA : ρB = 3 : 1

Core[2 marks]

Ice has density 0.92 g/cm³. Explain why icebergs float in sea water (1.03 g/cm³).

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Method: Compare.

Ice is less dense than sea water

Extended[1 mark]

Two liquids that do not mix have densities 0.80 g/cm³ and 1.26 g/cm³. State which forms the top layer.

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Method: The less dense liquid floats on top.

The 0.80 g/cm³ liquid

Extended[2 marks]

Oil (0.92 g/cm³), water (1.00 g/cm³) and syrup (1.33 g/cm³) are poured into a jar and do not mix. State the order from top to bottom.

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Method: Lower density floats higher.

Oil (top), water, syrup (bottom)

Extended[2 marks]

A plastic bead of density 0.95 g/cm³ is placed in a jar of oil (0.92 g/cm³) floating on water (1.00 g/cm³). State where the bead settles and why.

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Method: Denser than oil, less dense than water.

At the oil–water boundary: it sinks through the oil but floats on water

Extended[2 marks]

Liquid A has mass 45 g and volume 50 cm³. Liquid B has mass 60 g and volume 50 cm³. The liquids do not mix. Determine which floats on the other.

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Method: Compare densities.

ρA = 0.900 g/cm³, ρB = 1.20 g/cm³; A floats on B

Extended[3 marks]

A 100 cm³ sample of a liquid of density 0.79 g/cm³ is mixed with nothing else and poured onto 100 cm³ of water. Calculate the mass of each liquid and state which is on top if they do not mix.

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Method: m = ρV for each.

Liquid: 79.0 g; water: 100 g; the 0.79 g/cm³ liquid is on top

Extended[2 marks]

Explain why hot air rises above cold air, in terms of density.

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Method: Expanded air less dense.

Hot air has expanded, so it is less dense than the cold air around it and floats upwards

Extended[2 marks]

A plastic ball (density 0.90 g/cm³) is placed in a liquid of density 0.79 g/cm³. State whether it floats or sinks and explain.

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Method: Compare densities.

It sinks, because it is denser than the liquid

Extended[3 marks]

A solid floats in liquid X but sinks in liquid Y. Liquid X has density 1.2 g/cm³. What can be said about the density of the solid and of liquid Y?

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Method: Compare.

Solid density < 1.2 g/cm³, and liquid Y is less dense than the solid (so Y < solid < 1.2 g/cm³)

Extended[2 marks]

Explain how a hydrometer could be used to compare liquid densities.

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Method: Floats higher in denser liquid.

It floats higher in a denser liquid, so the depth it sinks to indicates the liquid's density

Extended[3 marks]

A drink layers into three bands: syrup (1.30 g/cm³), juice (1.05 g/cm³) and cream (0.98 g/cm³). A grape (1.10 g/cm³) is dropped in. State where the grape settles.

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Method: Between juice and syrup.

At the boundary between the juice and the syrup

Challenge questions

Harder, multi-step questions at the top end of the exam. Attempt these once you are confident with the questions above.

ChallengeCore[4 marks]

A crown of mass 1.20 kg displaces 75 cm³ of water. Pure gold has density 19.3 g/cm³. Calculate the crown's density and decide whether it is pure gold.

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Method: ρ = m/V.

ρ = 1200 ÷ 75 = 16.0 g/cm³; less than 19.3, so it is not pure gold

ChallengeCore[4 marks]

A hollow metal ball has outer volume 50 cm³ and mass 158 g. The metal has density 7.9 g/cm³. Calculate the volume of the hollow space inside.

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Method: Volume of metal = m/ρ.

Metal volume = 20.0 cm³; hollow = 50 − 20 = 30.0 cm³

ChallengeCore[4 marks]

A measuring cylinder of mass 140 g contains 60 cm³ of oil (density 0.90 g/cm³). Water is added to make a total of 100 cm³ (the liquids do not mix). Calculate the total mass.

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Method: Add masses.

Oil 54 g + water 40 g + cylinder 140 g = 234 g

ChallengeCore[3 marks]

A 2.0 m × 1.5 m sheet of glass is 4.0 mm thick and has density 2500 kg/m³. Calculate its mass.

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Method: V in m³.

V = 2.0 × 1.5 × 0.004 = 0.0120 m³; m = 30.0 kg

ChallengeCore[4 marks]

An alloy is made from 300 g of copper (8.9 g/cm³) and 100 g of zinc (7.1 g/cm³). Assuming volumes add, calculate the density of the alloy.

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Method: Total m ÷ total V.

V = 33.7 + 14.1 = 47.8 cm³; ρ = 400 ÷ 47.8 = 8.37 g/cm³

ChallengeExtended[3 marks]

A block floats in water (1.00 g/cm³) with exactly 60% of its volume submerged. Suggest its density and explain.

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Method: Floating: weight = weight of water displaced.

0.60 g/cm³: the mass of water displaced (0.60 × V × 1.0) equals the block's mass

ChallengeExtended[4 marks]

Three liquids are poured into a tall jar: A (40 g, 50 cm³), B (63 g, 50 cm³), C (50 g, 50 cm³). They do not mix. State the order from the top and where a bead of density 1.1 g/cm³ will settle.

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Method: Calculate densities.

A 0.80, C 1.0, B 1.26 g/cm³: top A, then C, bottom B; the bead settles at the C–B boundary

ChallengeExtended[3 marks]

Explain why a steel ship floats but a solid steel block sinks.

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Method: Average density.

The ship's hull encloses air, so its average density (mass ÷ total volume) is less than that of water; the solid block's density is 7.9 g/cm³

ChallengeExtended[4 marks]

A balloon filled with helium (0.18 kg/m³) has volume 0.020 m³ and the rubber has mass 3.0 g. Air density is 1.2 kg/m³. Calculate the average density of the balloon and state whether it rises.

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Method: Total mass ÷ volume.

Mass = 3.6 g + 3.0 g = 6.6 g; ρ = 0.0066 ÷ 0.020 = 0.330 kg/m³ < 1.2, so it rises

ChallengeExtended[3 marks]

Explain why ice forming on a lake starts at the surface and why this helps fish survive.

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Method: Ice less dense.

Ice is less dense than water, so it floats and forms a layer that insulates the water beneath, which stays liquid

All IGCSE Physics topics ← 1.3 Mass and Weight 1.5.1 Effects of Forces →

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