If a container is filled with ice to the brim, what happens to the level of water when the ice completely melts?

Analyze the question: A container is filled to the brim with ice (floating in water). When the ice melts, does the water level rise, fall, or stay the same? This tests Archimedes' principle and the flotation of ice.

Concept: A floating body displaces its own weight of liquid. Ice floats, so the weight of water displaced by the ice equals the weight of the ice itself.

Step-by-step solution:

1. Let the mass of the ice be m.
2. Floating ice displaces water of mass m, so the volume of water displaced is V_displaced = m / ρ_water.
3. When the ice melts, it becomes water of the same mass m. The volume of this melted water is V_melt = m / ρ_water.
4. Since V_displaced = V_melt, the melted ice exactly fills the space that the submerged part of the ice was occupying.
5. The part of the ice above the water level is also accounted for, because the ice's weight is entirely supported by the displaced water. Nothing extra is added to the total volume.

So the water level does not change, and no water spills over the brim.

(Note: the density of ice is less than that of water, so ice expands on freezing. The part of the ice above the surface is exactly compensated by the shrinkage in volume of the ice as it melts.)

Checking the options:

• A. Goes up: wrong, the melted ice only fills the space it already displaced.
• B. Water overflows: wrong, for the same reason.
• C. Level remains unchanged: correct.
• D. Drops: wrong, there is no loss of mass or net volume.

Answer: C

Exam tip: Remember "floating ice, same level". Floating ice displaces its own weight of water, so melting changes nothing. (If the ice were resting on the bottom or held down, or if it were ice on land melting into the sea, the result would differ.)