Cylinders – GCSE Maths

Foundation and Higher · Grade 4 · Calculator

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A cylinder is a prism with a circular end, so volume $=\pi r^{2}h$. Curved surface area is the label unrolled: circumference $\times$ height $=2\pi rh$. Total surface area adds the two circles: $2\pi r^2+2\pi rh$. Always halve a given diameter before you start.

In terms of $\pi$ means leave $\pi$ in the answer. Otherwise $\pi$-button and 3 s.f. A hollow pipe is a large cylinder minus a small one (same height, different radii). Capacity questions may want litres: divide cm³ by $1000$.

A cylinder is a circular prism: $V=\pi r^{2}h$. Curved surface $=2\pi rh$ (the label round the tin). Total surface adds the two circles: $2\pi rh+2\pi r^2$. Diameter 10 means radius 5 — that slip doubles or halves everything.

Objectives

• Volume = πr²h.
• If you are given the diameter, halve it before you square.
• The curved surface unrolls to a rectangle of width 2πr and height h.

Key points

• Use $V=\pi r^{2}h$ for the volume of a cylinder.
• Find the curved surface area ($2\pi rh$) and total surface area ($2\pi r^2+2\pi rh$).
• Halve a diameter to get the radius before using any formula.
• Leave an answer in terms of $\pi$ when asked, e.g. $160\pi$ cm³.

Worked examples

Questions and answers

GCSE Maths cylinders questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Forgetting to square the radius.

   The area of the end is πr², not πr.

2. Using the diameter as r.

   Halve the diameter.

3. Adding the ends when the question asked only for the curved surface.

   Read which surface is wanted.

Exam tips

• A calculator is useful here. Show the calculation you typed, not only the final line.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Write the formula with numbers substituted ($\pi \times 4^2\times 10$) before pressing anything — that line is a method mark.
• If the question says 'in terms of $\pi$', do not press the $\pi$ button at all; just collect the numbers.

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

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Questions students ask

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More on Cylinders

• Cylinders worked examples and method
  The method in order, key facts and the full lesson explanation
• Cylinders practice questions
  A second set of questions with answers, plus quick checks

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Last updated 9 November 2026.