Answer
$\frac{40\pi}{3}\approx41.89$ in
Work Step by Step
We know that the length of the arc $s$ cut off by $\theta$ can be calculated as $s=r\theta$.
We are given that $\theta=240^{\circ}$ and $r=10$ in.
To convert $\theta$ to radians, we must multiply $\theta$ by $\frac{\pi}{180}$.
$\theta=240^{\circ}=240(\frac{\pi}{180})=\frac{240\pi}{180}=\frac{4\pi}{3}$
Therefore, $s=\frac{4\pi}{3}(10)=\frac{4\pi}{3}\times10=\frac{4\pi\times10}{3}=\frac{40\pi}{3}\approx41.89$ in.
