The circle below has center O, and its radius is 6cm. Given that =m∠AOB50°, find the length of the minor arc AB.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.
Question
The circle below has center O, and its radius is 6cm. Given that =m∠AOB50°, find the length of the minor arc AB.Give an exact answer in terms of π, and be sure to include the correct unit in your answer.
Solution
The length of an arc on a circle is given by the formula:
Arc length = (θ/360) * 2πr
where:
- θ is the measure of the angle subtended by the arc at the center of the circle (in degrees),
- r is the radius of the circle.
Given that θ = 50° and r = 6 cm, we can substitute these values into the formula to find the length of the minor arc AB:
Arc length = (50/360) * 2π * 6 = (5/36) * 12π = (5/3)π cm
So, the length of the minor arc AB is (5/3)π cm.
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