GCSE & IGCSE maths practice

Arc length and sector area questions and answers

A sector is a "slice" of a circle with angle $\theta$ . It's $\dfrac{\theta}{360}$ of the whole circle, so arc length $= \dfrac{\theta}{360} \times 2\pi r$ and sector area $= \dfrac{\theta}{360} \times \pi r^2$ . The perimeter of a sector is the arc length plus the two radii.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Circles: lesson Arc length and sector area calculator

Where arc length and sector area comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: calculate arc lengths, angles and areas of sectors of circles.
Cambridge IGCSE (0580)	Core: arc length and sector area where the sector angle is a factor of 360°. Extended: any angle, including major sectors.

The method

Fraction of the circle = θ ÷ 360.
Arc length = fraction × 2πr.
Sector area = fraction × πr².
Perimeter = arc + 2 radii.
Finding θ: put the values in and solve.

Arc length and sector area questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

A sector has radius 6 cm and angle $90°$ . Find its arc length, to 3 significant figures.

Question 2Warm-upFoundation

A sector has radius 10 cm and angle $72°$ . Find its area, to 3 significant figures.

cm²

Exam-style

Question 3Exam-styleFoundation

A sector has radius 5 cm and angle $120°$ . Find its area in terms of $\pi$ .

cm²

Question 4Exam-styleFoundation

A sector has radius 8 cm and angle $45°$ . Find its arc length in terms of $\pi$ .

Question 5Exam-styleFoundation

A sector has radius 9 cm and angle $80°$ . Find its perimeter, to 3 significant figures.

Question 6Exam-styleFoundation

A sector of radius 10 cm has area $30\pi$ cm². Find the angle of the sector.

Challenge

Question 7ChallengeFoundation

A sector has radius 7 cm and arc length 11 cm. Find its angle, to 1 decimal place.

Question 8ChallengeFoundation

Find the area of a major sector with radius 4 cm and angle $300°$ , to 3 significant figures.

cm²

Common mistakes

Using the diameter in place of the radius.
Forgetting the two radii in the perimeter.
Mixing up the arc length and area formulas.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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