Free Circles, arcs & sectors questions for IGCSE Mathematics (0580), part of Mensuration. Each question has the answer and the marking points an examiner would look for.
Generate a full Circles, Arcs & Sectors worksheet →All Mensuration questionsA sector of radius 8 cm has area 30 cm². Find the angle of the sector and the arc length.
| Part | Answer and marking points | Marks |
|---|---|---|
| 53.7°; 7.5 cm θ360 × π × 82 = 30 M1 θ = 53.7° A1 arc = θ360 × 2πr M1 7.5 cm A1 | 4 |
Two circles, each of radius 6 cm, are drawn so that each circle passes through the centre of the other.
Find the exact area of the region inside both circles.
Find the exact perimeter of the overlapping region.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 24π − 18√3 cm² the centres and an intersection point form an equilateral triangle M1 angle at each centre subtended by the common chord = 120° A1 segment area = sector − triangle = 12π − 9√3 M1 sector 120°: 13 × 36π = 12π A1 triangle ½ × 6 × 6 × sin 120° = 9√3 A1 overlap = 2 segments = 24π − 18√3 A1 | 6 |
| (b) | 8π cm two arcs each 13 of the circumference M1 8π A1 | 2 |
The diagram shows a sector of a circle.
Calculate the area of the sector.
Calculate the perimeter of the sector.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 12.6 cm² 40360 × π × 62 M1 12.6 A1 | 2 |
| (b) | 16.2 cm 40360 × 2 × π × 6 M1 + 2 × 6 M1 16.2 A1 | 3 |
OAB is a sector of a circle with centre O, radius 6 cm and angle AOB = 120°.
Find the exact area of the segment between the chord AB and the arc AB. Give your answer in the form aπ − b√3.
Find the exact perimeter of the segment.
The segment is the cross-section of a prism of length 10 cm. Find the exact volume of the prism.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 12π − 9√3 cm² sector = 120360 × π × 62 = 12π M1 triangle = ½ × 6 × 6 × sin 120° M1 = 9√3 A1 12π − 9√3 A1 | 4 |
| (b) | 4π + 6√3 cm arc = 120360 × 2π × 6 M1 chord AB = 6√3 (cosine rule or right-angled triangles) M1 4π + 6√3 A1 | 3 |
| (c) | 120π − 90√3 cm³ 120π − 90√3 B1 | 1 |
A sector of radius 8 cm has area 60 cm². Find the angle of the sector and the arc length.
| Part | Answer and marking points | Marks |
|---|---|---|
| 107°; 15 cm θ360 × π × 82 = 60 M1 θ = 107° A1 arc = θ360 × 2πr M1 15 cm A1 | 4 |
A sector of a circle has radius 9 cm and angle 60°.
Find the arc length.
Find the perimeter of the sector.
Find the area of the sector.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 9.42 cm 60360 × 2π × 9 M1 9.42 A1 | 2 |
| (b) | 27.4 cm 27.4 B1 | 1 |
| (c) | 42.4 cm² 60360 × π × 92 M1 42.4 A1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in