Question

the circle shown has center $o$ and a radius of 3 inches. if angle $aob$ measures $120^{\circ}$, what is the length of arc $ab$, in inches?
$\pi$

Explanation:

Step1: Recall arc length formula

The formula for arc length is $s = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle, and $r$ is the radius.

Step2: Substitute given values

$\theta = 120^\circ$, $r = 3$ inches.
Expression: $s = \frac{120^\circ}{360^\circ} \times 2\pi \times 3$

Step3: Simplify the expression

First simplify $\frac{120^\circ}{360^\circ} = \frac{1}{3}$, then calculate $2\pi \times 3 = 6\pi$.
Expression: $s = \frac{1}{3} \times 6\pi = 2\pi$

Answer:

$2\pi$ inches