Question

The water level in a small aquarium reaches up to a mark A. After a large ice cube is dropped into the water, the cube floats and the water level rises to a new mark B. What will happen to the water level as the ice melts? Explain.

Answer 1

In the first case, we have an ice cube of mass, say m, floating in the water. Since it is floating, it would have to displace enough water to support its weight. Its volume, $\text{v =}\frac{m}{d}$, where m is the mass of the ice cube, and $\text{d}$ is the density of water.

In the second case, when the ice starts to melt, it turns into the water of volume,
$\text{v =}\frac{m}{d}$ which is the same volume it displaced before. So, the added volume is the same, so the level of the water will not change in the aquarium.

As a matter of fact, as long as objects are floating (i.e. they don't sink to the bottom of the liquid), they displace enough water to support their mass. Also, by changing from solid to liquid, the mass of water does not change, it will keep displacing the same amount of water.