Paper 2 structured question: Circles, arcs and sectors
Paper 2Core or Extended Mathematics6 marks
Diagram Description
Circle with radius 7 cm and central angle 60°
A circle has radius 7 cm. A sector of the circle has a central angle of 60°. Calculate the circumference, area, arc length of the sector, and the area of the sector. Express all answers in terms of π where appropriate.
| Quantity | Formula | Calculation | Answer |
|---|---|---|---|
| Circumference | 2πr | 2 × π × 7 | 14π cm |
| Area | πr² | π × 7² | 49π cm² |
| Arc length | (θ/360) × 2πr | (60/360) × 2 × π × 7 | (1/6) × 14π = 14π/6 = 7π/3 cm |
| Sector area | (θ/360) × πr² | (60/360) × π × 7² | (1/6) × 49π = 49π/6 cm² |
- a[1]
Calculate the circumference of the circle in terms of π.
- b[1]
Calculate the area of the circle in terms of π.
- c[2]
Calculate the length of the arc corresponding to the 60° sector, in terms of π.
- d[2]
Calculate the area of the sector with central angle 60°, in terms of π.