Overflowing ice cube experiment

Fill a glass with water and then add ice cubes so that they are sticking out above the brim of the glass. Make sure all ice cubes are floating in the water.

Observe what happens to the water level when the ice cubes melt. Does the water level overflow?

Explantation
This is a classic experiment with intriguing results. Observation reveals that the water will not over flow, even though the ice was initially above the top of the glass.

IF you freeze a glass of water, the ice will rise about the top of the brim because water expands as it freezes. If this ice melted, it would not over flow the glass, but would return to its original level. The expansion of water as it freezes makes it less dense than liquid water. Since the same mass occupies more volume, it becomes less dense.

Gram per cubic centimeter

If you examine the floating ice cubes, you will see that they are approximately 92% immersed underwater. This tells us that the density of ice is .92 g/cc (gram per cubic centimeter). IF an object is 10% immersed underwater, its volume would be .10g/cc (gram per cubic centimeter). it is easy to estimate the density of object by measuring what percentage of the object is immersed underwater.

According to Pascal’s Principle of Flotation, floating objects displace a mass of water equal to their own weight. IF a ten ton sip is floating, it will displace ten tons of water. Archimedes’ Principle states that the buoyant force that a fluid exerts on an object is equal to the weight of the water that objects displaces. So the buoyant force acting on a ten ton floating ship is ten tons, which is exactly equal not only to the weight of water displaced but also to the weight of the ship itself.

If we assume each ice cube has a mass of 20 grams, this means each ice cube is displacing 20 grams of water. If 92% of the ice cube is underwater, this means 18.4 grams of ice cube is underwater and 1.6 grams of the ice cube is above water.

Yet the ice cube is displacing 20 grams of water in the glass, since it has a mass of 20 grams

So when the ice cube melts, it does not overflow since it was already displacing 20 grams of water when it was an ice cube.

And, of course, a 20 gram ice cube will melt into a 20 grams of water.

So the water level can not possibly overflow, because a 20 gram floating ice cube and 20 grams of liquid water take up the same amount of space in the glass of water.