Ball Resting on Hollow Cylinder

Cylinder height $h = 3\text{ cm}$, volume $\pi r^2 h = 9\pi \implies r^2(3) = 9 \implies r = \sqrt{3}$. Ball radius $R = 2\text{ cm}$. When sphere rests on top rim of radius $r = \sqrt{3}$, the distance from center of sphere to top plane of cylinder is $\sqrt{R^2 - r^2} = \sqrt{2^2 - (\sqrt{3})^2} = 1\text{ cm}$. Topmost point of ball is $R = 2\text{ cm}$ above center of sphere. So topmost point is $1 + 2 = 3\text{ cm}$ above the top of the cylinder. Distance from base = cylinder height + $3\text{ cm} = 3 + 3 = 6\text{ cm}$.