Question

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

Explanation:

Step1: Recall arc length formula

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

Step2: Identify given values

Radius \(r = 18\) cm, central angle \(\theta = \frac{\pi}{3}\) radians.

Step3: Substitute values into formula

\(s = 18 \times \frac{\pi}{3}\)

Step4: Calculate the result

\(s = 6\pi\)

Answer:

A. \(6\pi\) cm