What happens when a glass is filled to the brim with water and an ice cube is in the glass already what would happen to the level of water when the ice cube had melted?

 When you fill a glass to the brim with water and have an ice cube floating in it, the level of the water will not overflow when the ice melts. This is because of the principle of displacement and the unique properties of water and ice.

Water expands when it freezes and becomes ice. Because of this expansion, ice is less dense than liquid water, which is why it floats. When you place an ice cube in a glass of water, it displaces an amount of water equal to the weight of the ice. This is Archimedes' principle, which states that a body submerged in a fluid experiences a buoyant force equal to the weight of the fluid that it displaces.

Since the ice is already floating in the water, the volume of water that it displaces is equal to the volume of the ice cube. When the ice melts, it will convert back into liquid water, taking up the same volume as the water it initially displaced when it was frozen. Therefore, the water level after the ice cube melts will remain the same, it will neither rise nor fall.