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Practice questions · Density and floating

Mass per unit volume.

Six original Cambridge-style questions on the definition and units, the three forms of the formula, floating and sinking, and the V = m / rho rearrangement.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Three forms, one check

ρ = m ÷ V, and its rearrangements.

01
[2 marks]

Define density and state two units in which it can be measured.

  • Density is the mass per unit volume (ρ = m ÷ V). ✓
  • Units: kg/m³ or g/cm³. ✓
02
Calculation
[2 marks]

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

ρ = m ÷ V = 540 ÷ 200

ρ = 2.7 g/cm³

03
Calculation
[2 marks]

A liquid has a density of 3.0 g/cm³. Calculate the volume occupied by 750 g of it.

V = m ÷ ρ = 750 ÷ 3.0

V = 250 cm³

V = m ÷ ρ, not ρ × m

04
Analysis
[2 marks]

An object has a density of 0.8 g/cm³. State whether it floats or sinks in water (1.0 g/cm³), and explain why.

  • It floats. ✓
  • Its density (0.8 g/cm³) is less than the density of water (1.0 g/cm³). ✓
05
Analysis
[3 marks]

To find a volume, a student rearranges ρ = m ÷ V into V = ρ × m. Explain why this is wrong, give the correct rearrangement, and use a units check to support it.

  • The correct rearrangement is V = m ÷ ρ. ✓
  • Multiplying ρ × m gives the wrong quantity. ✓
  • Units check: g ÷ (g/cm³) = cm³ (a volume), whereas g × (g/cm³) does not. ✓
06
Calculation
[2 marks]

A material has a density of 2.5 g/cm³. Calculate the mass of a 40 cm³ sample.

m = ρ V = 2.5 × 40

m = 100 g

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.