Which way will the Sphere rotate? Let's say we have a sphere, with an "inner boarder" splitting it into 4 equal parts. We extract the air from the 3/4 parts (leaving them completely empty) and we fill just 1/4 part with air. We then drop the sphere into into the Sea like so:
Light Gray Area: Empty
Red Area: Air-Filled
Dark Area: Border splitting the sphere into 4 equal parts

Would the Sphere rotate causing the Red Part to be on top or at the bottom of the Sphere?
 A: There are two forces on the ball, the buoyant force and the force of gravity. We want to know how the ball will rotate, so we want to know the resulting torque around its center.
We have to remember that the buoyant force is the result of water pressure against the surface of the ball. The water can't see inside the ball, only the outside. Since the outside is symmetric, the buoyant force will be directed straight up through the center of the ball. This provides zero torque.
The force of gravity, on the other hand, will push straight down through the center of mass, which is somewhere in the red region, away from the center of the ball. This causes non-zero torque. 
Hence, the torque will only be zero when the center of mass is directly above or below the geometric center of the ball. Technically, the forces and torques could balance with the red region on top as well as on the bottom, but it's not stable at the top. If we tilt the red region away from the top even slightly the gravitational torque will pull it down. In practice, then, the ball will settle with the red region on the bottom.
