GCSE · Circles, arcs & sectors

Arc length & sector areaExam-style questions

Why a sector is just a fraction of the whole circle, arc length and sector area from that one idea, perimeter of a sector (don't forget the radii), and working backwards from an arc or area to the angle.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The diagram shows sector $OPQ$ of a circle with centre $O$ . $OP = 9$ cm

The perimeter of the sector is $(18 + 4\pi)$ cm.

Work out, in terms of $\pi$ , the area of the sector.

Give your answer in its simplest form.

(4 marks)
Level 4 · 4 marksTry it
2
A sector of a circle has radius $14$ cm and arc length $18.5$ cm.

Work out the angle of the sector. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
3
A sector of a circle has area $45$ cm² and angle $100°$ .

Work out the radius of the circle. Give your answer correct to 3 significant figures.
Level 4 · 3 marksTry it
4
A sector of a circle of radius $12$ cm has area $24\pi$ cm².

(a) Work out the angle of the sector.

(b) Work out the arc length of the sector. Give your answer in terms of $\pi$ .
Level 4 · 4 marksTry it