Volume of a Cylinder

GCSE Geometry volume cylinder
Practice this formula All formulas
\( V=\pi r^2 h \)

Statement

The volume of a cylinder is given by:

\[ V = \pi r^2 h \]

where \(r\) is the radius of the circular base and \(h\) is the perpendicular height.

Why it’s true

  • Volume = base area × height.
  • The base of a cylinder is a circle, with area = \(\pi r^2\).
  • So, volume = \(\pi r^2 h\).

Recipe (how to use it)

  1. Find the radius of the circular base.
  2. Square it: \(r^2\).
  3. Multiply by \(\pi\).
  4. Multiply by height \(h\).
  5. Answer in cubic units.

Spotting it

Look for 3D “tube” shapes — circular cross-section, same size along the height.

Common pairings

  • Surface area of a cylinder.
  • Unit conversions (litres ↔ cm³ ↔ m³).

Mini examples

  1. Given: \(r=3\), \(h=10\). Find: Volume. Answer: \(90\pi\).
  2. Given: \(r=7\), \(h=4\). Find: Volume. Answer: \(196\pi\).

Pitfalls

  • Using diameter instead of radius (remember: radius = half of diameter).
  • Forgetting to square the radius.
  • Confusing surface area with volume.

Exam strategy

  • Write the formula before substituting numbers.
  • Check if height given is perpendicular, not slant.
  • Leave answers in terms of \(\pi\) unless decimals are required.

Summary

The volume of a cylinder is the product of its base area and its height: \(V=\pi r^2 h\). Always check whether you’re given diameter or radius, and cube your units.