Answer
$\frac{1}{2}$ m
Work Step by Step
We know that the length of the arc $s$ cut off by $\theta$ can be calculated as $s=r\theta$. Therefore, we also know that $r=\frac{s}{\theta}$.
We are given that $\theta=180^{\circ}$ and $s=\frac{\pi}{2}$ m.
We can convert $\theta$ to radians by multiplying $\theta$ by $\frac{\pi}{180}$.
$\theta=180^{\circ}=180(\frac{\pi}{180})=\frac{180\pi}{180}=\pi$
Therefore, $r=\frac{\frac{\pi}{2}}{\pi}=\frac{\pi}{2}\times\frac{1}{\pi}=\frac{\pi}{2\pi}=\frac{\pi\div\pi}{2\pi\div\pi}=\frac{1}{2}$ m.