Answer
$\frac{16}{5\pi}=\approx1.02$ km
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 $\theta=225^{\circ}$ and $s=4$ km.
We can convert $\theta$ to radians by multiplying $\theta$ by $\frac{\pi}{180}$.
$\theta=225^{\circ}=225(\frac{\pi}{180})=\frac{225\pi}{180}=\frac{5\pi}{4}$
Therefore, $r=\frac{4}{\frac{5\pi}{4}}=4\times\frac{4}{5\pi}=\frac{4\times4}{5\pi}=\frac{16}{5\pi}=\approx1.02$ km.
