Question

in circle o, central angle aob measures \frac{\pi}{3} radians. what is the length of arc ab? 6\pi cm 12\pi cm 18\pi cm 36\pi cm

Explanation:

Step1: Recall the arc - length formula

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

Step2: Identify the values of \(r\) and \(\theta\)

From the problem, the radius \(r = 18\) cm and the central angle \(\theta=\frac{\pi}{3}\) radians.

Step3: Substitute the values into the formula

Substitute \(r = 18\) and \(\theta=\frac{\pi}{3}\) into \(s=r\theta\). Then \(s=18\times\frac{\pi}{3}\).
Calculate \(18\times\frac{\pi}{3}=\frac{18\pi}{3}=6\pi\)

Answer:

\(6\pi\) cm (the first option)