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GCSE density calculations

Find density from dimensions, water displacement or liquid measurements; convert density units.

Practise

Water displacement

A fully submerged, non-porous solid raises a measuring-cylinder reading from 37 cm³ to 83 cm³. Its mass is 124.2 g. Find its density in g cm⁻³. Give your answer to 3 significant figures.

Before 37 cm³After 83 cm³Solid mass 124.2 g
Water readings before 37 cm³ and after 83 cm³. Fully submerged solid has mass 124.2 g. Levels are schematic; use the stated readings.
Larger diagram
Before 37 cm³After 83 cm³Solid mass 124.2 g

Treat the given values as exact unless an uncertainty is stated.

Use decimals or e notation, e.g. 4.2e-3. Enter the unit separately.

Hint

The solid’s volume is the increase in cylinder reading.

Worked solution
  1. V = 83 − 37 = 46 cm³.
  2. ρ = 124.2 / 46 g cm⁻³.
  3. Answer: 2.70 g cm⁻³ (3 significant figures).
Another question
Question type: Water displacement
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Foundation and Higher: this set covers content common to both tiers. Some calculations need several steps.

Mass and volume

Density is mass divided by volume. Use kg with m³ for kg m⁻³, or g with cm³ for g cm⁻³. A liquid’s mass excludes its container. For displacement, subtract the initial reading from the final reading. At constant mass an increase in volume reduces density. These questions use exact supplied readings; experimental uncertainty is discussed in the density practical guide.

Work through the practical method and sample results

GCSE scope

AQA 8463: 4.3.1.1; required practical 5 (selected); OCR Gateway J249: P1.1d–f; PM1.1i; PAG P1 (selected). Tasks cover the selected skills listed above.

AQA specification · OCR Gateway specification

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