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Geometry & Measures · Foundation & Higher

Volume of prisms

A prism is a 3D shape with a constant cross-section. Volume = area of cross-section × length.

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Key facts to remember

  • 1A prism has the same cross-sectional shape all the way through.
  • 2Volume of any prism = Area of cross-section × Length (or height).
  • 3Common prisms: cuboid (rectangular cross-section), cylinder (circular cross-section), triangular prism.
  • 4Volume units: cm³, m³. Capacity: 1 litre = 1000 cm³.
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Formulas

Volume of prism
V = A × l

A = area of cross-section, l = length

Volume of cylinder
V = πr²h
Volume of cuboid
V = l × w × h
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Worked examples

Example 1

A triangular prism has a right-angled triangular cross-section with legs 4 cm and 6 cm, and length 10 cm. Find the volume.

Working

  1. Area of triangle = ½ × 4 × 6 = 12 cm²
  2. Volume = 12 × 10 = 120 cm³
Answer120 cm³
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Common mistakes

✗Using the wrong face as the cross-section — it must be the face that stays the same along the length.
✗Forgetting to halve when the cross-section is a triangle.
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Exam tips

✓Identify and calculate the cross-section area first, then multiply by the length.
✓Draw and label the cross-section separately if the diagram is confusing.

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