My wife and I were cookin' a Cajun feast for the anniversaire de ma mere. While I handled the vittles, the lovely and talented Mrs. Boy made the drinks.
  She had made the tea strong and wanted to dilute it with 4 cups of water but the guests were at the door and the tea was still hot so she decided to dilute it with ice instead.
  She turned to me and said, "Fat, sweetie, how many ice cubes make a cup of water?"
  I confessed that I did not know as I had not measured the water when I made the cubes. To make matters worse I had not paid attention to how full I had made the trays so we couldn't just refill them and see how much they held.
  Things seemed desperate, as I'd die before I'd serve my Gumbo without sweet tea, but Mrs. Boy is no fool and she found a way. The tea was just right (though the cheese grits were a little burnt).

How did Mrs. B manage to ascertain the proper number of ice cubes to produce the 4 cups of water needed to dilute the tea? All she had to use was the ice cubes themselves, an ungraduated glass pitcher of unknown volume and the 4 cup graduated Pyrex measuring cup full of (too strong) tea.

An object floats in liquid because its density is lower than that of the liquid.  Density is mass per unit volume, and, when constant (density of h20 can be taken to be constant in this context, and so can the density of ice.), the density can relate volume to mass.<o:p></o:p>

<o:p> </o:p>

For convenience, let density of h20=1.  To float, the density of the ice must be less than 1; Pick any number, c<1, which will suffice (note c>0 also).<o:p></o:p>

<o:p> </o:p>

Ice is made by freezing liquid water.  Take a cup of water, and freeze it.  The result will be an equal MASS of ice (freezing does not change mass), with volume of (1cup)/c; a volume slightly greater than 1 cup.<o:p></o:p>

<o:p> </o:p>

If the resulting ice cube is place in liquid water, it will float by displacing an equal mass of h20, or 1 cup, since that volume represents the original mass of the water before it was frozen into ice. So the level of the water will rise up an additional cup on the scale of the measuring cup.  Note that th top of the ice cube will be above the level of the water, but that is immaterial in this context.

<o:p> </o:p>

A practical observation that we have all made that gives empirical evidence for his result is the following:  Put some ice in a glass and then fill it with water or any liquid, to the brim.  Set it out, and when the ice melts, the level of the water will still be at the brim, neither higher nor lower.  Ever see a glass OVERFLOW as the ice melts?  Can't happen.