A modern aluminum sculpture consists of a hollow cylinder that is capped on one end by a solid hemisphere. The cylinder has an outer diameter of 100 cm and thickness of 1 cm, and the hemisphere has the same diameter as the outside of the cylinder.

If, on a level surface, the sculpture balances in stable equilibrium at any point on its hemispherical surface, how long is the cylinder, and what is the minimum ceiling height in the museum to permit the sculpture to assume any stable position?