# What is the length of an arc of a 12-inch radius circle that subtends a central angle of `pi/6` ? Arc length in a circle is based on the circle's circumference, which is defined by the formula `C=2pir` , where C represents circumference and r represents radius. For a circle with radius 12 inches, the circumference is

`C=2pir=2pi(12)=24pi~~75.4` inches

Since the measure of the central angle that forms the arc...

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Arc length in a circle is based on the circle's circumference, which is defined by the formula `C=2pir` , where C represents circumference and r represents radius. For a circle with radius 12 inches, the circumference is

`C=2pir=2pi(12)=24pi~~75.4` inches

Since the measure of the central angle that forms the arc is `pi/6` and a full circle contains `` radians, the desired arc is `(pi/6)/(2pi)=1/12` of the entire circle's circumference. Therefore, the arc length is

`1/12*C=1/12*24pi=2pi~~6.28` inches

The length of the arc is `2pi` inches, or approximately 6.28 inches.

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