How do you find the radian measure of the central angle of a circle of radius 6 inches that intercepts an arc of length 27 inches?

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How do you find the radian measure of the central angle of a circle of radius 6 inches that intercepts an arc of length 27 inches?

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Answer 1 · 2016-12-12T11:18:47

Arc of $27$ $27$ inches will subtend a central angle of $4.5$ $4.5$ radian.

Explanation:

The circumference of the circle is $2 \cdot π \cdot r = 2 \cdot π \cdot 6 = 12 π$ $2*pi*r = 2*pi*6=12pi$ inches, which subtends central angle of $2 π$ $2pi$ radian.

Therefore arc of $27$ $27$ inches will subtend a central angle of $27/(12cancelpi)*2cancelpi = 27/6 =4.5$ radian.[Ans]

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How do you find the radian measure of the central angle of a circle of radius 6 inches that intercepts an arc of length 27 inches?

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