Question

the radius of a circle is 8 kilometers. what is the length of an arc that subtends an angle of \\( \frac{\pi}{3} \\) radians?
give the exact answer in simplest form.
kilometers

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 \(r = 8\) kilometers and \(\theta=\frac{\pi}{3}\) radians.
Substitute into \(s = r\theta\), we get \(s=8\times\frac{\pi}{3}\).

Answer:

\(\frac{8\pi}{3}\) kilometers