What is density and how is it calculated in the context of Cambridge IGCSE Coordinated Science?

Density is a measure of how much mass is contained in a given volume. It is calculated using the formula: Density = Mass/Volume. In the Cambridge IGCSE Coordinated Science curriculum, understanding density is crucial for solving problems related to motion and material properties.

How does density affect the motion of objects in fluids?

Density plays a significant role in determining whether an object will float or sink in a fluid. An object will float if its density is less than the density of the fluid it is placed in. Conversely, it will sink if its density is greater. This principle is essential in understanding buoyancy and is a key concept in the Cambridge IGCSE Coordinated Science syllabus.

Why is understanding density important in the study of motion?

Understanding density is important in the study of motion because it affects how objects interact with their environment. For example, in fluid dynamics, the density of a fluid can influence the resistance an object experiences as it moves through the fluid. This concept is crucial for students studying motion in the Cambridge IGCSE Coordinated Science course.

What are some common methods for measuring the density of an irregularly shaped object?

To measure the density of an irregularly shaped object, one common method is to use water displacement to determine its volume. By submerging the object in water and measuring the volume of water displaced, you can calculate the object's volume. Then, using the object's mass, you can calculate its density. This method is often discussed in the Cambridge IGCSE Coordinated Science curriculum.

How does temperature affect the density of substances?

Temperature can significantly affect the density of substances. Generally, as temperature increases, the density of a substance decreases because the particles move faster and spread apart, increasing the volume. This concept is important in understanding various phenomena in motion and is covered in the Cambridge IGCSE Coordinated Science syllabus.

Why is "Mixing g/cm³ and kg/m³ without converting" a common mistake in Density?

Why it happens: Mass given in grams, volume in cm³, but answer required in SI base units. How to avoid it: Convert at the start: 1\,g/cm^3 = 1000\,kg/m^3. Or work consistently in g and cm³, then convert the final answer.

Why is "Reading the final water level rather than the change in water level as volume" a common mistake in Density?

Why it happens: Forgetting to subtract the initial water level. How to avoid it: V_solid = V_final - V_initial. Write this explicitly before substituting numbers.

Why is "Stating an object floats because it is 'light'" a common mistake in Density?

Why it happens: Everyday language; students do not reference density. How to avoid it: Floating depends on density relative to the fluid, not absolute mass. A massive ship floats; a tiny stone sinks.

Cambridge IGCSE Coordinated Science (0654)

Density

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Short Notes - Density

Detailed Study Notes

Detailed notes on Motion for Cambridge IGCSE Coordinated Science, covering key concepts, explanations, examples, and exam-focused revision points.

Density — Cambridge IGCSE Coordinated Science 0654

Density explains why some objects float and others sink. Cambridge tests the formula ρ = m/V, experimental methods to find density of regular and irregular solids, and why substances have different densities.

At a glance

Density ρ = m/V. Units: kg/m³ or g/cm³. 1 g/cm³ = 1000 kg/m³.
Water density: 1000 kg/m³ = 1 g/cm³. Objects less dense than water float.
Regular solid: measure dimensions with ruler/calipers → calculate volume. Irregular: displacement (eureka can) method.
Gases are much less dense than liquids/solids because particles are far apart.
Ice floats on water because it is less dense than liquid water (ρ_ice ≈ 917 kg/m³ < ρ_water = 1000 kg/m³).

What you’ll learn

Mapped to the Cambridge IGCSE 0654 syllabus (2025-2027).

P1.4a — Define density and use the formula ρ = m/V.
P1.4b — Describe experimental methods to measure density of regular and irregular objects.
P1.4c — Relate density to floating and sinking.

Density Formula and Units

ρ = m/V. Learn both unit systems and how to convert.

Density:

ρ = m / V

ρ (rho) = density (kg/m³ or g/cm³)
m = mass (kg or g)
V = volume (m³ or cm³)

Rearrangements:

m = ρV
V = m/ρ

Unit conversion:

1 g/cm³ = 1000 kg/m³
Water: ρ = 1 g/cm³ = 1000 kg/m³

Typical densities:

Material	Density (kg/m³)
Air	1.2
Wood (oak)	700
Water	1000
Aluminium	2700
Iron/Steel	7900
Lead	11 300
Gold	19 300

Floating and sinking:

Object floats if its average density < density of fluid
Object sinks if its average density > density of fluid
A hollow steel ship floats because its average density (including air) < water density

ρ = m/V. Unit: kg/m³ (or g/cm³). 1 g/cm³ = 1000 kg/m³.
Object floats if density < fluid density; sinks if density > fluid density.
Water density: 1000 kg/m³ (the reference).

Measuring Density

Regular solids use geometry for volume; irregular solids use water displacement.

Regular solid (e.g., rectangular block):

Measure mass with a balance (kg or g)
Measure dimensions with ruler or vernier calipers
Calculate volume: V = l × w × h (for cuboid)
Calculate ρ = m/V

Irregular solid (e.g., stone):

Measure mass with a balance
Fill a measuring cylinder with water; read initial volume V₁
Submerge the solid (use thread to lower it); read new volume V₂
Volume of solid = V₂ − V₁
Calculate ρ = m/(V₂ − V₁)

Eureka can method (for large irregular objects):

Fill eureka can to the spout with water
Lower the object into the can; water overflows into a measuring cylinder
Volume of overflow = volume of object

Liquid density:

Measure mass of an empty measuring cylinder (m₁)
Add a known volume V of liquid; measure new mass (m₂)
ρ = (m₂ − m₁) / V

Regular solid: volume from dimensions. Irregular solid: water displacement.
Eureka can: overflow water volume = object volume.
Liquid: measure mass of known volume.

Quick recap

ρ = m/V. 1 g/cm³ = 1000 kg/m³. Water = 1000 kg/m³.
Regular solid: calculate volume from dimensions. Irregular: use water displacement.
Float if ρ_object < ρ_fluid. Sink if ρ_object > ρ_fluid.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

ρ = m/V — density (kg/m³) = mass (kg) / volume (m³).
Water density — 1000 kg/m³ = 1 g/cm³.
Irregular solid volume — measure by water displacement in measuring cylinder.
Unit conversion — 1 g/cm³ = 1000 kg/m³.

How it’s examined

Paper 4: 'A stone has a mass of 120 g and volume of 40 cm³. Calculate its density in g/cm³' (2 marks — ρ = 120/40 = 3 g/cm³). 'Describe how you would measure the density of an irregular stone using a displacement method' (4 marks — mass on balance; fill measuring cylinder; record volume; submerge stone; record new volume; V = difference; ρ = m/V). 'Will the stone float or sink in water? Justify' (2 marks — sinks because density 3 g/cm³ > 1 g/cm³ of water).

Sources: Cambridge IGCSE Coordinated Sciences 0654 syllabus 2025-2027 (P1); 0654 Examiner Reports 2022-2024. Last reviewed 2026-05-14.

Take this whole topic with you

Step-by-step worked examples — Density

Step-by-step solutions to past-paper-style questions on density, written exactly the way a tutor would explain them at the board.

1Density of a regular solid
Core• density, regular solid
Question
A steel block has dimensions $4.0\,\text{cm} \times 3.0\,\text{cm} \times 2.0\,\text{cm}$ and a mass of $188\,\text{g}$ . Calculate its density in $\text{kg/m}^{3}$ .
Step-by-step solution
1. Step 1
  Find the volume.
  $V = 4.0 \times 3.0 \times 2.0 = 24.0\,\text{cm}^{3} = 24.0 \times 10^{-6}\,\text{m}^{3}$
2. Step 2
  Convert mass to kg.
  $m = 188\,\text{g} = 0.188\,\text{kg}$
3. Step 3
  Apply $\rho = m/V$ .
  $\rho = \dfrac{0.188}{24.0 \times 10^{-6}} = 7833\,\text{kg/m}^{3} \approx 7800\,\text{kg/m}^{3}$
Answer
$\rho \approx 7800\,\text{kg/m}^{3}$
Examiner tip
Always check units — the question may give cm and g but ask for kg/m³. Convert before substituting.
2Density of an irregular solid by displacement
Extended• density, irregular solid, displacement method
Question
A stone has a mass of $240\,\text{g}$ . When lowered into a measuring cylinder partially filled with water, the water level rises from $50\,\text{cm}^{3}$ to $140\,\text{cm}^{3}$ . Calculate the density of the stone.
Step-by-step solution
1. Step 1
  Volume of stone = volume of water displaced.
  $V = 140 - 50 = 90\,\text{cm}^{3}$
2. Step 2
  Apply $\rho = m/V$ .
  $\rho = \dfrac{240}{90} = 2.67\,\text{g/cm}^{3}$
Answer
$\rho = 2.67\,\text{g/cm}^{3}$ (or $2670\,\text{kg/m}^{3}$ )
3Will the object float? — reasoning with density
Challenge• floating, sinking, density comparison
Question
Object A has density $800\,\text{kg/m}^{3}$ and object B has density $1200\,\text{kg/m}^{3}$ . Both are placed in water ( $\rho_{\text{water}} = 1000\,\text{kg/m}^{3}$ ). Predict and explain the behaviour of each.
Step-by-step solution
1. Step 1
  Object A: $\rho_{A} = 800\,\text{kg/m}^{3} < \rho_{\text{water}}$ .
  $\text{Upthrust when fully submerged} > \text{weight} \Rightarrow \text{floats}$
2. Step 2
  Object B: $\rho_{B} = 1200\,\text{kg/m}^{3} > \rho_{\text{water}}$ .
  $\text{Weight} > \text{maximum upthrust} \Rightarrow \text{sinks}$
Answer
A floats (density less than water); B sinks (density greater than water).
Examiner tip
Explain in terms of upthrust vs weight, not just 'density is less/more than water'.

Key Formulae — Density

The formulae you need to memorise for density on the Cambridge IGCSE 0654 paper, with every variable defined in plain English and a note on when to use it.

Density
$\rho = \dfrac{m}{V}$
$\rho$
density (kg/m³ or g/cm³)
$m$
mass (kg or g)
$V$
volume (m³ or cm³)
When to use
Any density, mass, or volume calculation.
Example
$\rho = \dfrac{240\,\text{g}}{90\,\text{cm}^{3}} = 2.67\,\text{g/cm}^{3}$

Key Definitions and Keywords — Density

Definitions to memorise and the exact keywords mark schemes credit for density answers — sharpened from recent examiner reports for the 2026 0654 sitting.

Density
Examiner keyword
The mass per unit volume of a substance. SI unit: $\text{kg/m}^{3}$ . Formula: $\rho = m/V$ .
Upthrust (buoyancy force)
Examiner keyword
The upward force exerted by a fluid on an object submerged (fully or partially) in it, equal to the weight of fluid displaced (Archimedes' principle).
Related: density, floating
Displacement method
A technique to find the volume of an irregular solid by measuring the volume of liquid it displaces when fully submerged.
Homogeneous material
A material with uniform composition throughout, so density is the same at every point.

Common Mistakes and Misconceptions — Density

The traps other students keep falling into on density questions — taken from recent Cambridge IGCSE 0654 examiner reports and mark schemes — and how to avoid them.

✕Mixing g/cm³ and kg/m³ without converting
Why it happens
Mass given in grams, volume in cm³, but answer required in SI base units.
How to avoid it
Convert at the start: $1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$ . Or work consistently in g and cm³, then convert the final answer.
✕Reading the final water level rather than the change in water level as volume
Why it happens
Forgetting to subtract the initial water level.
How to avoid it
$V_{\text{solid}} = V_{\text{final}} - V_{\text{initial}}$ . Write this explicitly before substituting numbers.
✕Stating an object floats because it is 'light'
Why it happens
Everyday language; students do not reference density.
How to avoid it
Floating depends on density relative to the fluid, not absolute mass. A massive ship floats; a tiny stone sinks.

Density — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Material

Density (kg/m³)

Air

1.2

Wood (oak)

700

Water

1000

Aluminium

2700

Iron/Steel

7900

Lead

11 300

Gold

19 300

Regular solid (e.g., rectangular block):

Measure mass with a balance (kg or g)
Measure dimensions with ruler or vernier calipers
Calculate volume: V = l × w × h (for cuboid)
Calculate ρ = m/V

Irregular solid (e.g., stone):

Measure mass with a balance
Fill a measuring cylinder with water; read initial volume V₁
Submerge the solid (use thread to lower it); read new volume V₂
Volume of solid = V₂ − V₁
Calculate ρ = m/(V₂ − V₁)

Eureka can method (for large irregular objects):

Fill eureka can to the spout with water
Lower the object into the can; water overflows into a measuring cylinder
Volume of overflow = volume of object

Liquid density:

Measure mass of an empty measuring cylinder (m₁)
Add a known volume V of liquid; measure new mass (m₂)
ρ = (m₂ − m₁) / V

Density

Short Notes - Density

Detailed Study Notes

At a glance

What you’ll learn

Density Formula and Units

Measuring Density

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Density of a regular solid

2Density of an irregular solid by displacement

3Will the object float? — reasoning with density

Density

Density

Upthrust (buoyancy force)

Displacement method

Homogeneous material

✕Mixing g/cm³ and kg/m³ without converting

✕Reading the final water level rather than the change in water level as volume

✕Stating an object floats because it is 'light'

Density — frequently asked questions

Density

Short Notes - Density

Detailed Study Notes

At a glance

What you’ll learn

Density Formula and Units

Measuring Density

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1Density of a regular solid

2Density of an irregular solid by displacement

3Will the object float? — reasoning with density

Density

Density

Upthrust (buoyancy force)

Displacement method

Homogeneous material

✕Mixing g/cm³ and kg/m³ without converting

✕Reading the final water level rather than the change in water level as volume

✕Stating an object floats because it is 'light'

Density — frequently asked questions