What is the radius of a circle with a central angle of 4π7 radians that intercepts an arc of length 12π inches?

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24-01-2018
Mathematics

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What is the radius of a circle with a central angle of 4π7 radians that intercepts an arc of length 12π inches?

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jamuuj jamuuj · Answer 1 · 2018-02-03T23:38:48+01:00

Radian measure is given by dividing the length of an arc by the radius of a given circle. Such that an arc that subtends an angle of 1 radian to the center of a circle is equivalent to the radius of the circle.
Therefore; θ = s/r where θ is the angle subtended in radians, s is the length of the arc and r is the radius of the circle.
Hence; r = s/θ
= 12π ÷ (4π/7)
= 12 × (7/4)
= 21 inches