As others have mentioned, water takes up *less* space than ice. Water is a somewhat unusual material that shrinks as it heats up (most things expand)
An interesting version of this experiment is to have an ice cube in a glass and then fill the glass up right to the brim with water and hypothesize what will happen as the ice melts. Some people will think the melted ice will just immediately overflow while other people who know that ice shrinks as it melts might think that the water level will reduce but in reality it stays at the same level because of buoyancy. It’s a good way illustration of several principals of physics.
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