A-level · Trigonometry

Arc length and sector areaExam-style questions

The radian formulas for arc length, sector area and segment area, where they come from, and using them in reverse — finding a radius or angle from a given perimeter or area, and the perimeters of sectors and segments.

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33 questions · A-level 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 $OAB$ of a circle of radius $5\text{ cm}$ with area $30\text{ cm}^2$ . Find
(a) the angle $AOB$ in radians,
(b) the perimeter of the sector.
Level 3 · 4 marksTry it
2
The diagram shows a circle of radius $6\text{ cm}$ in which the chord $AB$ subtends an angle of $\frac{\pi}{3}$ at the centre $O$ . Find the exact area of the shaded minor segment.
Level 3 · 3 marksTry it
3
The diagram shows a circle of radius $7\text{ cm}$ in which the chord $AB$ subtends an angle of $1.4$ radians at the centre. Find the area of the shaded minor segment, giving your answer to 3 significant figures.
Level 3 · 2 marksTry it
4
The diagram shows a sector $OAB$ of a circle of radius $8\text{ cm}$ with angle $AOB = \frac{\pi}{2}$ . The chord $AB$ is drawn, cutting off the shaded segment. Find the exact perimeter of the shaded segment.
Level 3 · 3 marksTry it
5
The diagram shows a sector with radius $r\text{ cm}$ , perimeter $28\text{ cm}$ and area $40\text{ cm}^2$ . Find the two possible values of $r$ . (The diagram is not accurately drawn.)
Level 3 · 4 marksTry it

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