Answer
The radius of the circle is 15.6 m.
Work Step by Step
Let $\theta$ be the angle in radians. Let $A$ be the area of the sector. Then the ratio of the angle to $2\pi$ is equal to the ratio of the sector area to the area of the whole circle.
$\frac{\theta}{2\pi} = \frac{A}{\pi ~r^2}$
$r^2 = \frac{2A}{\theta}$
$r = \sqrt{\frac{2A}{\theta}}$
$r = \sqrt{\frac{(2)(64~m^2)}{(\pi/6)}}$
$r = 15.6~m$
The radius of the circle is 15.6 m.
