You have a cube of ice floating in a glass of water. The question is what fraction of the ice will be above the water line? Assume that the ice is not bobbing.

Most of you have probably heard the answer to this before. But please provide a proof or solution, along with your assumptions.

As the question states what type of water, it is up to our assumption whether it is a cup of river water or sea water.  Thus, the solution is uncertainty.

A small ice cube, let's say, 1 cubic centimeter you place in the water will float awhile but melt.  It still floats.  A minute later, it melt and nothing is left.  So how could there be any ice cube in the water then.  Nothing is left and still uncertainty.

When we look at the puzzle, we must not look at one angle.  But another angle.  Your question does not state the size of the ice cube.  It is still our imagination to give answer.

Anyway, the answer is uncertainty.