Question

the circle shown has center o and a radius of 3 inches. if angle aob measures 120°, what is the length of arc ab, in inches? a π b 2π c 3π d 6π

Explanation:

Step1: Convert angle to radians

We know that $120^{\circ}=120\times\frac{\pi}{180}=\frac{2\pi}{3}$ radians.

Step2: Use arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius and $\theta$ is the central - angle in radians. Given $r = 3$ inches and $\theta=\frac{2\pi}{3}$, then $s=3\times\frac{2\pi}{3}$.

Step3: Calculate the arc - length

$s = 2\pi$ inches.

Answer:

B. $2\pi$