jmc

We begin by drawing a diagram:

Let the radius of the sphere be $r$. We see the radius of the cylinder is $r$ and the height of the cylinder is $2r$. Thus, from the cylinder's volume we have $$60=\pi (r^2)(2r)=2\pi r^3.$$ Dividing both sides by 2 yields $\pi r^3=30$. The volume of the sphere is $$\frac{4}{3}\pi r^3=\frac{4}{3}(30)=\boxed{40}$$ cubic centimeters. (Notice that we didn't have to solve for $r$!)