Arcs and sectors · Year 10
In Year 10 you learn: arc length and area of a sector.
A sector is a “slice” of a circle between two radii, and an arc is the curved part of its edge. Because a sector is a fraction of the whole circle (angle ÷ 360), its arc length and area are that same fraction of the circumference and area.
Key facts
- Fraction of the circle = θ ÷ 360.
- Arc length = (θ ÷ 360) × 2πr.
- Sector area = (θ ÷ 360) × πr².
- Perimeter of a sector = arc length + 2r.
- Segment area = sector area − triangle area (triangle = ½r² sin θ).
Worked examples
Example 1
A sector has radius 8 cm and angle 45°. Find its arc length and its area, to 1 d.p.
Answer: Arc 6.3 cm, area 25.1 cm²
Example 2
Find the perimeter of a sector with radius 10 cm and angle 72°, to 1 d.p.
Answer: 32.6 cm
Example 3
A sector of radius 6 cm has an arc length of 5 cm. Find its angle, to the nearest degree.
Answer: 48°