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 a sector of a circle, centre $O$ , radius $6.5$ cm. The angle of the sector is $110°$ .Diagram NOT accurately drawn

(a) Work out the area of the sector. Give your answer correct to 3 significant figures. (3 marks)

(b) Work out the arc length of the sector. Give your answer correct to 3 significant figures. (1 mark)
Level 3 · 4 marksTry it
2
The diagram shows a sector of a circle, centre $O$ .

The radius of the circle is $8$ cm and the angle of the sector is $140°$ .Diagram NOT accurately drawn

Work out the perimeter of the sector.

Give your answer correct to 3 significant figures. (4 marks)
Level 3 · 4 marksTry it
3
The diagram shows a sector of a circle of radius $12$ cm. The angle of the sector is $75°$ .Diagram NOT accurately drawn

(a) Work out the arc length of the sector. Give your answer correct to 1 decimal place.

(b) Work out the area of the sector. Give your answer correct to 1 decimal place.
Level 3 · 4 marksTry it
4
The diagram shows a sector of a circle of radius $8$ cm. The angle of the sector is $135°$ .Diagram NOT accurately drawn

Work out the perimeter of the sector. Give your answer correct to 1 decimal place.
Level 3 · 3 marksTry it
5
A sector of a circle has radius $9$ cm and angle $40°$ .

(a) Work out the arc length of the sector. Give your answer in terms of $\pi$ .

(b) Work out the area of the sector. Give your answer in terms of $\pi$ .
Level 3 · 4 marksTry it

1 more question on arc length & sector area

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