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Geometry & Measures · Higher

Volume of prisms & cylinders

Volume measures the 3D space inside a shape. For any prism (including cylinders), Volume = Area of cross-section × length (or height). You must be able to find volumes of various prisms and cylinders, and work backwards to find missing dimensions.

Revising volume of prisms & cylinders the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Volume of prisms & cylinders GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Volume of any prism = cross-sectional area × length.
  • 2Volume of a cylinder = πr²h, where r is radius and h is height.
  • 3The cross-section is the shape you see when you slice the prism perpendicular to its length.
  • 4For compound prisms, split into simpler shapes, find each area, then multiply by length.
  • 5Units: if dimensions are in cm, volume is in cm³; if in m, volume is in m³.
  • 61 litre = 1000 cm³; 1 m³ = 1,000,000 cm³.
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Formulas

Volume of any prism
V = A × l

A = area of cross-section, l = length

Volume of a cylinder
V = πr²h
Volume of a triangular prism
V = ½ × b × h × l
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Worked examples

Example 1

A cylinder has radius 4 cm and height 10 cm. Find its volume. Give your answer in terms of π.

Working

  1. Identify the formula: V = πr²h
  2. Substitute values: V = π × 4² × 10
  3. Calculate: V = π × 16 × 10 = 160π
Answer160π cm³
Example 2

A prism has a cross-sectional area of 15 cm² and a length of 8 cm. Find its volume.

Working

  1. Use V = A × l
  2. V = 15 × 8 = 120 cm³
Answer120 cm³
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Common mistakes

✗Using diameter instead of radius in the cylinder formula.
✗Forgetting to square the radius (writing πrh instead of πr²h).
✗Mixing up the cross-section area with the total surface area.
✗Not converting units consistently (mixing cm and m).
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Exam tips

✓Always identify the cross-section first — it's the shape repeated along the length.
✓If given a diameter, halve it to get the radius before using V = πr²h.
✓Show all working — write the formula, substitute values, then calculate.
✓"Give your answer in terms of π" means leave π in your answer, don't multiply by 3.14.

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