Question

a circle has a radius of 4 inches. find the length of the arc intercepted by a central angle of 240°.

Explanation:

Step1: Convert degrees to radians

First, convert the central - angle from degrees to radians. The conversion formula is $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 240^{\circ}$, then $\theta_{rad}=240\times\frac{\pi}{180}=\frac{4\pi}{3}$.

Step2: Use the arc - length formula

The arc - length formula is $s = r\theta$, where $s$ is the arc length, $r$ is the radius of the circle, and $\theta$ is the central angle in radians. Given $r = 4$ inches and $\theta=\frac{4\pi}{3}$, then $s=4\times\frac{4\pi}{3}=\frac{16\pi}{3}$ inches.

Answer:

$\frac{16\pi}{3}$ inches