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Practice questions · Measuring density

Measure, displace, divide.

Six original Cambridge-style questions on measuring a regular solid, the displacement method, the all-important subtract-the-initial-volume step, and full density calculations.

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.
The two routes

Volume from a ruler, or from a rise.

01
Analysis
[3 marks]

Describe how to find the density of a small regular metal cube.

  • Measure the length of one side with a ruler and calculate the volume (side cubed). ✓
  • Find the mass on a balance. ✓
  • Calculate density = mass ÷ volume. ✓
02
Analysis
[4 marks]

Describe how to find the density of a small irregular stone using a measuring cylinder, water and a balance.

  • Part fill the cylinder with water and read the initial volume. ✓
  • Lower the stone in fully and read the new, higher volume. ✓
  • Volume of the stone = final reading − initial reading. ✓
  • Find the mass on a balance, then density = mass ÷ volume. ✓
03
Calculation
[3 marks]

A measuring cylinder reads 25 cm³. A pebble of mass 60 g is added and the level rises to 45 cm³. Calculate the density of the pebble.

Volume. 45 − 25 = 20 cm³

ρ = m ÷ V = 60 ÷ 20

ρ = 3.0 g/cm³

04
Analysis
[2 marks]

In the previous experiment, a student divides the mass by the final reading of 45 cm³ instead of the rise. Explain why this is wrong.

  • The 45 cm³ includes the water that was already there, not just the pebble. ✓
  • The pebble's volume is only the rise (the final reading minus the initial reading), so dividing by 45 gives a density that is too small. ✓
05
Calculation
[3 marks]

A rectangular metal block measures 2.0 cm by 3.0 cm by 5.0 cm and has a mass of 81 g. Calculate its density.

Volume. 2.0 × 3.0 × 5.0 = 30 cm³

ρ = m ÷ V = 81 ÷ 30

ρ = 2.7 g/cm³

06
Calculation
[3 marks]

A cylinder holds 50 cm³ of water. A metal object of mass 49.5 g is lowered in, raising the level to 68 cm³.

(a)State the volume of the object. (b)Calculate its density.

(a) 68 − 50 = 18 cm³

(b) ρ = 49.5 ÷ 18

ρ = 2.75 g/cm³

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.