Find the arc length of a sector of a circle with a radius of 5 inches and a central angle of 120°.
Question
Find the arc length of a sector of a circle with a radius of 5 inches and a central angle of 120°.
Solution
The formula to find the arc length of a sector is given by:
Arc length = (central angle/360) * 2πr
where:
- central angle is the angle subtended by the arc at the center of the circle,
- r is the radius of the circle.
Given:
- central angle = 120°,
- r = 5 inches.
Substituting these values into the formula, we get:
Arc length = (120/360) * 2π * 5 Arc length = (1/3) * 2π * 5 Arc length = (2/3) * π * 5 Arc length = 10/3 * π Arc length ≈ 10.47 inches.
So, the arc length of the sector is approximately 10.47 inches.
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