Question

find the length of the arc of a circle of radius 9 inches subtended by a central angle of \frac{4}{3}\pi radians. answer exactly in terms of pi. inches question help: video written example message instructor

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 \(r = 9\) inches and \(\theta=\frac{4}{3}\pi\) radians.
Substitute into \(s = r\theta\): \(s=9\times\frac{4}{3}\pi\).

Step3: Simplify the expression

First, calculate \(9\times\frac{4}{3}\). Since \(9\div3 = 3\), then \(3\times4=12\). So \(s = 12\pi\).

Answer:

\(12\pi\)