The radius of a circle is 6 inches.  If the central angle is 5pi/3, find the length of the intercepted arc.

2 Answers

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flbyrne | (Level 3) Assistant Educator

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To find the length of the arc, multiply the angle in radians by the radius.

arc length=`thetar`     (1)

where `theta` is the angle and r is the radius of the circle

For a whole circle, the angle is `2pi` , so the length of the arc is `2pir`

Substitute `(5pi)/3` for `theta` and 6 inches for r in (1):

arc length=`((5pi)/3)*6=10pi`

Therefore the arc length is `10pi`