Question

in a circle with a radius of 3 ft, an arc is intercepted by a central angle of \frac{2\pi}{3} radians. what is the length of the arc? 2\pi ft 3\pi ft 6\pi ft 9\pi ft

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc is \(s = r\theta\), where \(s\) is the arc length, \(r\) is the radius of the circle, and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 3\) ft and \(\theta=\frac{2\pi}{3}\) radians. Substitute these values into the formula \(s=r\theta\):

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Step3: Simplify the expression

Cancel out the common factor of 3 in the numerator and denominator: \(s = 2\pi\) ft.

Answer:

\(2\pi\) ft