Solution: The volume of a hemisphere is $ \frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi 27x^3 = 18\pi x^3 $. The cylinder's volume is $ \pi x^2 \cdot 3x = 3\pi x^3 $. The ratio is $ \frac{18\pi x^3}{3\pi x^3} = \boxed{6} $.