Suppose you fill a glass with ice cubes. When the ice cubes melt, is the glass still full?

Well, you can't "fill" the glass with ice cubes to begin with.

The ice cubes never fit together perfectly, and there are always

a lot of air-spaces between them. When the ice melts, there is

almost exactly the same amount of air in the glass as there was

originally. (Actually, a tiny bit more, for other reasons.)