6/10, pass the exam

Oral presentation + course work question, 3 hours -_-!!
An interesting question was asked...
The last question is a "joke" question, which P said it would not be something relevant in advance. The question is -- I could hardly believe what I heard at first -- if an ice-cube is floating on a cup of full water, when the ice melts, would the water overflow? I said it would not, theoretically. Then he asked me to show why... I drawn a picture, and said something about density, volumn, ... sadly I do not have the exact phrase for wording. Then he asked about the assumptions I was making. He asked why with global warming, people would worry about the rise of sea level. I said the iceberg does not necessarily float on the sea. Bingo, he then said in his original question, it could also be possible that the ice is seated at the floor of the cup, depending on the relative size and shape of the ice-cube and the cup. J jumped in and said that was a problem of the definition of "floating". ^_^

Then P asked me how to prove it, if all of us do not know whether the water will overflow. My mind is running more slowly now... I said, maybe by experiments. He asked, how to do that. I said, consider situations, make other factors as irrelevant to the problem as possible, and do the experiment. I felt lucky that I saw him nod his head when I mentioned that was only an "observation", and we might want to repeat it for many times. Then his said that the reality would be more complicated, for example, we might expect problems of measuring the level of water, "how full" it is, etc., and other factors (such as surface force?) occur when we choose different sizes and shapes of the cup or ice-cube...