Solution: The volume of a sphere is $\frac{4}{3}\pi (2x)^3 = \frac{4}{3}\pi (8x^3) = \frac{32}{3}\pi x^3$. The volume of a hemisphere is $\frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi (27x^3) = 18\pi x^3$. The ratio of the volumes is: