Discussion
When a cube of ice floating on water in a beaker melts, the level of water in the beaker
Answer: C
The water level remains the same.
By Archimedes' principle, floating ice displaces a weight of water equal to its own weight. When the ice melts it becomes water of exactly that weight, and so it fills exactly the volume it was already displacing.
\[ \begin{aligned} m_{\text{ice}} &= \rho_{w} V_{\text{displaced}} \\ V_{\text{melt}} &= m_{\text{ice}} / \rho_{w} = V_{\text{displaced}} \end{aligned} \]
The level would rise only if the ice held something denser than water that floated with it, or fall if it held air pockets that escaped; for pure ice in fresh water it neither rises nor falls.
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