An arc is a fraction of the circumference: A sector with angle θ out of a full circle (360°) covers a fraction θ/360 of the full circumference.
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Worked example — arc length
Find the arc length of a sector with radius 9 cm and angle 80°.
Step by step
- Apply the formula.
Final answer
Arc length = 4π ≈ 12.6 cm.
Worked example — find the radius
A sector has arc length 15 cm and angle 60°. Find its radiu.
Step by step
- Write the formula and substitute.
- Solve for r.
Final answer
r ≈ 14.3 cm.
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Perimeter includes two radii: The perimeter of a sector is the arc length PLUS the two straight edges (the radii) that border it.
Worked example — perimeter
Find the perimeter of a sector with radius 12 cm and angle 120°.
Step by step
- Arc length.
- Perimeter = arc + 2 radii.
Final answer
Perimeter ≈ 49.1 cm.
Worked example — sprinkler coverage
A garden sprinkler rotates through 140° and reaches 8 m. Find the total length of the arc it cover.
Step by step
- Apply the arc length formula.
Final answer
Arc length ≈ 19.5 m.