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.

I too agree with you'll that buoyant force could stabilise the shape of the ice to float on the water.  However, the question mentions a glass of water and it does not mention that the water must not be added with salt or other substances.  For instance, if salt is added to the water, the density of the water would change and this would affect the fraction of ice that is to be exposed above the water.  As the question does not give the assumption that it must be pure water, there is an uncertainty of what fraction of ice cube to be exposed above the water.

Not only that the question does not mention that you must only add one ice cube in the cup.  For instance, if you add more than half cup of ice cubes in the cup, many ice cubes would sink and none of them expose in the air.  The answer is still turned up to be uncertainty since some float and some sink and not all expose.

The question never mentions the size of the ice cube.  For instance, if you take a cubic centimeter of ice cube to place it in the cup, it melts entirely and you could not see any within a minute.  The answer for this question turns up to be nil since there is no fraction of ice cube appears above the water line as a result of all melt.

Subject to the uncertainty of the question, the answer is obvious.  Uncertainty!