Answer
The radius of the circle is approximately $868 \space m$.
Work Step by Step
Formula for the area of a circular sector: $$A = \frac 12 r^2 \theta$$
Solving for the radius: $$2A = r^2 \theta$$ $$\frac{2A}{\theta} = r^2$$ $$r = \pm \sqrt{\frac{2A}{\theta}}$$ *Negative radiuses do not exist. $$r = \sqrt {\frac{2A}{\theta}}$$
A = 50 $m ^2$
$\theta = angle = \frac{11\pi}{6}$
$$r = \sqrt {\frac{2(50 \space m^2)}{\frac{11 \pi}6}} \approx 868 \space m$$
