Year 10 Maths — Areas related to circles

Find the arc length, area and perimeter of a sector, and the area of a segment.

Name: ________________________

1.Doubling a sector's radius while keeping its angle at the centre the same multiplies its area by what?
- a) 2
- b) 3
- c) 8
- d) 4
2.A sector of a circle of radius 6 cm has an angle of 60° at the centre. Take π = 3.14. What is its area, in square centimetres?
3.In a circle of radius 10 cm a sector has an angle of 90° at the centre. Take π = 3.14. The triangle made by the two radii and the chord joining their ends has an area of 50 square centimetres. What is the area of the minor segment cut off by that chord, in square centimetres?
4.A quadrant is a sector with an angle of 90° at the centre. Take π = 22/7. What is the area of a quadrant of a circle of radius 14 cm, in square centimetres?
5.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. What is its area, in square centimetres?
6.A sector of a circle of radius 7 cm has an angle of 90° at the centre. Take π = 22/7. How long is its arc, in centimetres?
7.The minute hand of a clock is 21 cm long. Take π = 22/7. What area does it sweep in 5 minutes, in square centimetres?
8.A sector of a circle of radius 21 cm has an angle of 60° at the centre. Take π = 22/7. How long is its arc, in centimetres?

Answer key — Year 10 Maths — Areas related to circles