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Arc and Sector
Middle School
Definition
An arc is a portion of the circle between two points. A sector is the region bounded by two radii and an arc.
Formulas
l = (θ)/(360°) × 2π r
Arc length (θ in degrees)
l = rθ
Arc length (θ in radians)
A = (θ)/(360°) × π r²
Sector area (θ in degrees)
A = (1)/(2)r²θ
Sector area (θ in radians)
Examples
Example 1
Find the arc length and area of a sector with radius 10cm and central angle 72°.
Applications
Engineering
Circular pipes, arc design
Graphics
Pie charts
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