Answer
1 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 $\theta=90^{\circ}$ and $s=\frac{\pi}{2}$ m.
We can convert $\theta$ to radians by multiplying $\theta$ by $\frac{\pi}{180}$.
$\theta=90^{\circ}=90(\frac{\pi}{180})=\frac{90\pi}{180}=\frac{\pi}{2}$
Therefore, $r=\frac{\frac{\pi}{2}}{\frac{\pi}{2}}=\frac{\pi}{2}\times\frac{2}{\pi}=\frac{2\pi}{2\pi}=\frac{2\pi\div2\pi}{2\pi\div2\pi}=\frac{1}{1}=1$ m.
