With advance apologies for not being an actual physicist, and for feeling intimidated by math beyond simple algebra, I would like to ask a question.

I've read that the mass of an object can be treated as belonging to a point that is the object's center of mass. Suppose a rigid object with the the mass and density of earth, but shaped like a cylinder, has the same volume of air and water that earth has.(let's say it has a height of 4 times the earth's radius.) Would its ocean and atmosphere be gathered in a spherical bulge around its equator, approaching its center of mass as closely as possible? Or would they be distributed over its entire surface, perhaps unevenly?