A sector is a slice of a circle, like a slice of pizza, and an arc is the curved edge of the sector. A sector with angle θ is the fraction θ/360 of the whole circle.
So arc length = θ/360 × 2πr and sector area = θ/360 × πr². For radius 13 cm and angle 43°: area = 43/360 × π × 169 = 63.4 cm². The perimeter of a sector is the arc length plus two radii.
Worked example
A sector has radius 6 cm and angle 270°. Find the arc length to 1 d.p.
- 270/360 = 3/4 of the circumference.
- 3/4 × 2π × 6 = 9π = 28.27…
Answer:28.3 cm
Key words
- sector
- a slice of a circle between two radii
- arc
- part of the circumference
- θ/360
- the fraction of the circle
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Common Core-referenced: HSG-C.B.5