jmc

If the triangle is rotated about the shorter leg, then the radius is the longer leg and the height is the shorter leg, and the volume is $$\frac{1}{3}\cdot (15^2\pi )(8)=600\pi \text{ cubic centimeters}.$$ If the triangle is rotated about the longer leg, then the radius is the shorter leg and the height is the longer leg, and the volume is $\frac{1}{3}(8^2\pi )(15)$, which is $\frac{8}{15}$ of the volume we found earlier. So, the maximum possible volume is $\boxed{600\pi }$ cubic centimeters.