Answer
4 cm
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 $\theta=\frac{\pi}{4}$ and $s=\pi$ cm.
Therefore, $r=\frac{\pi}{\frac{\pi}{4}}=\pi\times\frac{4}{\pi}=\frac{4\pi}{\pi}=\frac{4\pi\div\pi}{\pi\div\pi}=\frac{4}{1}=4$ cm.