Question

find the length of the arc of a circle of radius 36 inches subtended by a central angle of $\frac{1}{6}pi$ radians. answer exactly in terms of pi. inches question help: message instructor submit question

Explanation:

Step1: Recall the arc - length formula

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

Step2: Substitute the given values into the formula

Given \(r = 36\) inches and \(\theta=\frac{1}{6}\pi\) radians.
Substitute into \(s = r\theta\): \(s=36\times\frac{1}{6}\pi\).

Step3: Simplify the expression

\(36\times\frac{1}{6}\pi=(36\div6)\pi = 6\pi\).

Answer:

\(6\pi\)