A glass of water has a 10-cm^3 ice cube floating in it. The glass is filled to the brim with col

step 1 Hello and welcome to this video solution of numerate. So here we are given that a glass of water

A glass of water has a 10-cm^3 ice cube floating in it. The...

A glass of water has a $10-\mathrm{cm}^{3}$ ice cube floating in it. The glass is filled to the brim with cold water. By the time the ice cube has
completely melted, how much water will have flowed out of the glass? The sp gr of ice is $0.92$.

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Key Concepts

Archimedes' Principle

This principle states that any object, wholly or partially immersed in a fluid, experiences an upward buoyant force equal to the weight of the fluid displaced by the object. It is crucial for understanding why floating objects displace a specific volume of liquid proportional to their weight.

Density and Buoyancy

The relationship between an object's density and the density of the fluid determines whether it will float or sink and what fraction of it will be submerged. For a floating body, the ratio of its density to that of the fluid indicates the proportion of the object submerged, directly linking density differences to buoyancy effects.

Phase Change and Conservation of Mass

When a substance undergoes a phase change, such as ice melting into water, its mass remains constant even though its volume may change due to differences in density between phases. This concept is key in determining how the volume of water resulting from melted ice compares to the volume it displaced while frozen.

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