Home / IGCSE 0625 / Motion, forces, energy / Density and floating
IGCSE 0625 / Section 1.4 / Core

How tightly the matter is packed.

A kilogram of feathers and a kilogram of lead have the same mass, yet one fills a sack and the other a thimble. Density measures how much mass is packed into each unit of volume, and it decides the most everyday question of all: will it float?

Concept mapDensity → Skill mapOpen the star map →
The key idea

Density is the mass per unit volume: ρ = m / V, measured in kg/m³ or g/cm³. An object floats in a fluid if its density is less than the density of the fluid, and sinks if its density is greater.

Definition · learn the exact words

Density is defined as mass per unit volume.

ρ = m / V

Units: kg/m³ or g/cm³. In words, it is how much mass sits in each unit of space.

Section 01

Will it float?

Change the object and the fluid, then predict. An object floats when it is less dense than the fluid it sits in, and sinks when it is denser. Watch how oil, water, and the object settle into layers by density.

Stage 1 · Learn

Check the meaning of density

Four quick checks on the definition, units, and floating. Each correct answer earns XP and lights this skill on your star map.

Quick check+10 XP

Density is defined as...

Quick check+10 XP

An object floats in a liquid if its density is...

Quick check+10 XP

Two balls have equal mass, but ball A has a larger volume than ball B. Ball A has...

Quick check+10 XP

A correct unit for density is...

Section 02

Reading a density value.

Water is the benchmark. Its density is 1.0 g/cm³. Anything less dense than water floats on it; anything denser sinks. A density value is just a ratio: pack more mass into the same volume and the number rises.

Worked example

A metal cube has a mass of 540 g and sides of length 3.0 cm. Find its density.

Step 1 · Volume of the cubeV = 3.0 × 3.0 × 3.0 = 27 cm³
Step 2 · Density from ρ = m / Vρ = 540 / 27 = 20 g/cm³
Step 3 · AnswerThe density is 20 g/cm³, far denser than water, so this cube sinks.
Examiner trap

Water is the benchmark, with a density of exactly 1.0 g/cm³. But what is that in kilograms per cubic metre? Because a cubic metre is so large, it takes 1000 kg/m³ of water to fill it. Do not let the large number fool you: 1.0 g/cm³ and 1000 kg/m³ are the same density. To convert g/cm³ to kg/m³, multiply by 1000.

Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 1.

Finish the four checks above to unlock the exam questions
Exam style+20 XP

A metal block has a mass of 240 g and a volume of 30 cm³. Its density is...

Exam style+20 XP

Water has a density of 1.0 g/cm³. Expressed in kg/m³, this is...

Exam style+20 XP

A solid of density 0.8 g/cm³ is lowered into water of density 1.0 g/cm³. It will...

Skill unlocked

Density and floating, mastered.

This skill is now lit gold on your star map. Keep the chain going.

-Rank -Level -Score -Topics
Go deeper · practice
Six original Cambridge-style questions
The definition and units of density, the ρ = m / V calculation, the floating and sinking rule, and the g/cm³ to kg/m³ conversion. Attempt each, then reveal the worked solution.
Stage 3 · master the unit
Motion, forces and energy challenge
Mixed questions across the whole unit, each one worth XP. Start this only when you feel confident across every topic in the unit, not just density.
Start the unit challenge →