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Ratio & Proportion · Foundation & Higher

Density, mass & volume

Density, mass and volume are connected by a formula triangle. Density is a measure of how much mass is packed into a given volume.

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Key facts to remember

  • 1Density = Mass ÷ Volume
  • 2Mass = Density × Volume
  • 3Volume = Mass ÷ Density
  • 4SI units: density in g/cm³ or kg/m³; mass in g or kg; volume in cm³ or m³.
  • 5A denser material has more mass per unit volume.
  • 6Water has a density of 1 g/cm³ — objects less dense than water float.
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Formulas

Density
D = M / V
Mass
M = D × V
Volume
V = M / D
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Worked examples

Example 1

A metal block has mass 540 g and volume 60 cm³. Find its density.

Working

  1. Density = Mass ÷ Volume
  2. D = 540 ÷ 60 = 9 g/cm³
Answer9 g/cm³
Example 2

A liquid has density 1.2 g/cm³ and mass 300 g. Find its volume.

Working

  1. Volume = Mass ÷ Density
  2. V = 300 ÷ 1.2 = 250 cm³
Answer250 cm³
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Common mistakes

✗Dividing mass by density to get density, or confusing which quantity to divide.
✗Using inconsistent units — ensure mass and volume units match the density units.
✗Forgetting to state the units in the answer.
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Exam tips

✓Use the formula triangle: cover the quantity you want, and the remaining two show whether to multiply or divide.
✓Always check your units — if density is in g/cm³, mass must be in g and volume in cm³.

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