The ice cube that melts in a full glass

Question

A glass of water is filled exactly to the brim, and an ice cube floats in it with part of the cube sticking up above the rim. When the ice cube melts completely, does the water overflow, does the level drop, or does it stay exactly at the brim? Explain using the principle that governs floating. Then: what if the ice cube contained a small pebble? What if it contained an air bubble?

Accepted Answer

The level stays exactly at the brim: no overflow. Archimedes. A floating ice cube pushes aside (displaces) exactly enough water to balance its own weight. So the water displaced by the cube weighs the same as the cube. When the cube melts, it turns into liquid water with the same weight, and water of that weight has exactly the volume that was displaced. The melted ice slots precisely into the hole the floating cube was occupying below the surface. The part of the cube above the surface was the "extra" volume ice has because it is less dense than water, and that extra volume disappears on mel…

The ice cube that melts in a full glass

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