Question

arc ab is $\frac{1}{3}$ of the circumference of a circle. what is the radian measure of the central angle?$\frac{pi}{3}$ radians$\frac{2pi}{3}$ radians$\frac{3pi}{2}$ radians$3pi$ radians

Explanation:

Step1: Recall full circle radians

A full circle has $2\pi$ radians.

Step2: Calculate fraction of circle

Arc AB is $\frac{1}{3}$ of the circumference, so the central angle is $\frac{1}{3}$ of $2\pi$.
<Expression>
$\text{Central angle} = \frac{1}{3} \times 2\pi = \frac{2\pi}{3}$
</Expression>

Answer:

$\frac{2\pi}{3}$ radians