GCSE Maths revision · Geometry and measures

Circles: circumference

Foundation and Higher

The idea

The circumference of a circle is $\pi d$ , or $2\pi r$ . The diameter is twice the radius. A semicircle's perimeter is half the circumference plus the diameter.

Find the radius or the diameter from what you are given.
Use $C = \pi d$ .
For a part circle, add the straight edges to the curved length.

Watch out Check whether you have the radius or the diameter before you substitute.

See it worked

Worked exampleNon-calculator1 mark

A region inside a circle is bounded by one chord and the shorter arc joining the ends of the chord. What is this region called?

A sector has two straight radius boundaries.
The boundary here is one chord and one arc, so the region is a segment.

Answer Segment

Your turn

Question 1Non-calculator3 marks

This question is about the parts of a circle.

(a) Write down the name of a straight line that touches a circle at exactly one point.

(b) Write down the name of the region between a chord and the arc it cuts off.

Question 2Non-calculator2 marks

A circular track has diameter 14 m. Work out its circumference. Give your answer exactly in terms of $\pi .$

Question 3Calculator allowed5 marks

The diagram shows a running track. It has two straight sections, each 80 m long, joined by two semicircular ends with the same radius $r$ metres.

The length of the track is 400 m.

(a) Work out the value of $r$ . Give your answer correct to 3 significant figures.

(b) A lane nearer the inside of the curves has semicircles of radius $(r - 1.2)$ m and the same straights. How much shorter is one lap of this lane? Give your answer correct to 3 significant figures.

In past papers

76 official questions in 71 papers since 2017. The latest:

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