symmetry in floating objects

[yasar1967]

Suppose we drop a bottle cork on water. It has a shape similar to -rougly- a pyramid i.e. upper area A1 is smaller than bottom A2. Therefore it's vertically as well as horizontally symmetric.
But as we drop it, it does not stay vertical but horizontal making upside and downside areas (A) equal.
Why? Why doesn't it stay vertical? Has it got to do with buoyant force and gravity? How?

[jimvoit]

If I understand you correctly, you are asking “Why doesn’t the cork remain with its axis of symmetry in the vertical?”. The answer to that is that in that position, the cork is in a state of unstable equilibrium, and any perturbation will upset it.