smc

Suppose that each side of the hexagon is $3$. Then the distance from each vertex of the hexagon to the center is also $3$, so that the circle has radius $3$. Since the circle has circumference $2\pi (3)=6\pi$, the arc intercepted by any side (which measures $60^{\circ }$) has length $\frac{1}{6}\ast 6\pi =\pi$, so that our answer is $\boxed{3:\pi }$ and we are done.