We have a full glass of water to the edge where an ice cube floats. What will happen when the ice melts?
Will the water level drop? Will some of the water overflow? Will the level not change?
The answer is that the water level is maintained. To understand this, we have to use physics. We all remember the Archimedes Principle that tells us that every body submerged in a fluid experiences a vertical and upward thrust equal to the weight of fluid dislodged. This means that when a body floats (as is the case with ice on water), its weight is equal to the weight of the volume of water dislodged, which corresponds to the volume of the submerged part of the ice.
On the other hand we know that water increases in volume when it freezes. This behavior is what causes the ice to float in the water. The volume increases, but the mass remains the same (if we freeze 1 kg. Of water, we will have 1 kg. Of ice, although it occupies more 1 kg. Of ice than 1 kg. Of water). Therefore, the volume of water that weighs the same as a piece of ice is a little smaller than the volume of that piece of ice. And what happens if the piece of ice melts in the water? When the ice melts, its volume decreases. How much does it decrease? Well, the same thing that increased when it froze. That is, when melted, its density is equal to that of the water in which it is immersed. It occupies the same volume as the water that had dislodged when it was ice. In other words; The melted water has the same volume as the submerged part of the ice. So if the volume contained in the glass is not modified, it will maintain its level.