Cambridge IGCSE Physics 0625

1.4 Density

Mass per unit volume, practical measurements and floating using density data.

CoreExtended
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2026-2028 syllabus

Syllabus checklist

Core

  1. Define density as mass per unit volume; recall and use ρ = m ÷ V.
  2. Describe how to determine the density of a liquid, a regularly shaped solid and an irregularly shaped solid that sinks in a liquid, including appropriate calculations.
  3. Determine whether an object floats based on density data.

Supplement

  1. Determine whether one liquid floats on another liquid from density data, given that the liquids do not mix.
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Key language

Definitions

Density

Mass per unit volume.

Displacement

The increase in liquid volume when a fully submerged object is placed in the liquid.

Regular solid

A solid whose volume can be calculated from measured dimensions.

Irregular solid

A solid whose volume is found by displacement because it has no simple volume formula.

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Core

Understanding density

Mass packed into a volume

Density compares how much mass is contained in a particular volume. A material with more mass in the same volume has a greater density.

Common density units are kg/m3 and g/cm3. The units used for mass and volume must match the required density unit.

MassVolumeDensity
kgm3kg/m3
gcm3g/cm3

Floating and sinking

Compare the object's average density with the liquid's density:

  • Object density less than liquid density: the object floats.
  • Object density greater than liquid density: the object sinks.
  • Object density equal to liquid density: the object can remain suspended within the liquid.

Example

An object has density 0.80 g/cm3 and is placed in water of density 1.0 g/cm3. Since 0.80 < 1.0, the object floats.

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Core equation

Density calculations

Density

ρ = mV
  • ρ: density (kg/m3 or g/cm3)
  • m: mass (kg or g)
  • V: volume (m3 or cm3)

Mass

m = ρV
  • Use when density and volume are known.
  • The mass unit follows the density unit.

Volume

V = mρ
  • Use when mass and density are known.
  • Keep all units consistent.

Rectangular solid

V = l × w × h
  • l: length
  • w: width
  • h: height
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Core practical methods

Determining density

Density of a liquid

Apparatus: balance, measuring cylinder and container.

  1. 1

    Measure the mass of the empty container, m1.

  2. 2

    Use a measuring cylinder to measure a known volume, V, of the liquid.

  3. 3

    Pour the liquid into the container and measure the total mass, m2.

  4. 4

    Calculate liquid mass: m = m2 − m1.

  5. 5

    Calculate density: ρ = m ÷ V.

Fig. 1: Finding liquid mass by subtraction before calculating density.

Density of a regularly shaped solid

Apparatus: balance and ruler or suitable length-measuring instrument.

  1. 1

    Measure the mass, m, using a balance.

  2. 2

    Measure the dimensions. For a cuboid, measure l, w and h.

  3. 3

    Calculate volume: V = l × w × h.

  4. 4

    Calculate density: ρ = m ÷ V.

Fig. 2: A regular solid whose volume is calculated from its dimensions.

Density of an irregular solid

Apparatus: balance, measuring cylinder, liquid and thread if needed.

  1. 1

    Measure the mass, m, using a balance.

  2. 2

    Record the initial liquid volume, V1, at eye level.

  3. 3

    Fully submerge the solid. Remove trapped air bubbles and record V2.

  4. 4

    Calculate solid volume: V = V2 − V1.

  5. 5

    Calculate density: ρ = m ÷ V.

Fig. 3: The volume of a sinking irregular solid is the rise in liquid volume.
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Supplement only

Non-mixing liquid layers

When liquids do not mix, they form layers arranged by density. The least dense liquid forms the top layer and the most dense forms the bottom layer.

Example

Oil has density 0.90 g/cm3 and water has density 1.0 g/cm3. If they do not mix, oil floats on water because 0.90 < 1.0.

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Cambridge-style practice

Practice questions

Core 1

Define density.

Density is mass per unit volume.

Core 2

A block has a mass of 240 g and a volume of 80 cm3. Calculate its density.

ρ = m ÷ V

ρ = 240 ÷ 80

ρ = 3.0 g/cm3

Core 3

A cuboid is 5.0 cm long, 4.0 cm wide and 3.0 cm high. Its mass is 120 g. Calculate its density.

V = 5.0 × 4.0 × 3.0 = 60 cm3

ρ = 120 ÷ 60

ρ = 2.0 g/cm3

Core 4

A stone has a mass of 84 g. It raises the water level from 50 cm3 to 80 cm3. Calculate its density.

Stone volume = 80 − 50 = 30 cm3

ρ = 84 ÷ 30

ρ = 2.8 g/cm3

Core 5

An object has density 850 kg/m3. Water has density 1000 kg/m3. State whether the object floats or sinks.

850 kg/m3 < 1000 kg/m3.

The object floats because it is less dense than water.

Extended 1

Three non-mixing liquids have densities 0.79 g/cm3, 1.00 g/cm3 and 1.26 g/cm3. State their order from top to bottom.

Least dense forms the top layer; most dense forms the bottom layer.

Top to bottom: 0.79 g/cm3, 1.00 g/cm3, 1.26 g/cm3.

Extended 2

Liquid A has density 920 kg/m3 and liquid B has density 1050 kg/m3. They do not mix. Which liquid is on top?

920 kg/m3 < 1050 kg/m3.

Liquid A is on top because it is less dense.

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