A glass of ice water is filled to the brim with water; the ice cubes stick up above the water surface. After the ice melts, which is true?

Question

BlackTom AI · Accepted Answer

Consider the scenario: a glass is filled to the brim with water and ice cubes protrude above the water surface. As the ice melts, its mass becomes liquid water.
Option 1 analyzes the situation by noting that when floating ice melts, the final liquid water volume equals the amount of water that was displaced by the submerged part of the ice, which keeps the water level from rising above the rim. Since there is no spill during melting, the level remains at or right at the top of the glass.
Option 2 claims that some water spills over the sides. This would require the water level to rise during melting, which does not occur because the melted ice occupies exactly the amount of space that was displaced by the submerged ice portion, leaving the level unchanged.
Option 3 argues that the outcome cannot be determined without densities. In fact, the qualitative result for floating ice is invariant to the exact densities: the melting process does not increase the water level beyond the rim in this setup.
Option 4 states the level ends below the top. This would imply a decrease in water level during melting, which contradicts the principle that meltwater from floating ice precisely compensates the displaced volume, keeping the level at the brim.
Thus, the reasoning for each choice hinges on how floating ice and its meltwater interact with the boundary of the container, particularly when the container starts full and no spill occurs during melting.

A glass of ice water is filled to the brim with water; the ice cubes stick up above the water surface. After the ice melts, which is true? 单项选择题

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