Answer
$\frac{2\pi}{3}\approx2.09$ mm
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 $\theta=30^{\circ}$ and $r=4$ mm.
To convert $\theta$ to radians, we must multiply $\theta$ by $\frac{\pi}{180}$.
$\theta=30^{\circ}=30(\frac{\pi}{180})=\frac{30\pi}{180}=\frac{\pi}{6}$
Therefore, $s=\frac{\pi}{6}(4)=\frac{\pi}{6}\times4=\frac{\pi\times4}{6}=\frac{4\pi}{6}=\frac{2\pi}{3}\approx2.09$ mm.
