Final answer:
Yes, a glass can be filled with water above its brim due to water's cohesive properties, thanks to hydrogen bonding among the molecules. The level of the water does not change when the ice melts because the melted ice occupies the same volume as the water it had displaced when frozen.
Step-by-step explanation:
A glass can indeed be filled with water to a level above its brim, and the same principle explains why the water won't necessarily overflow when the ice in a glass melts. This occurs due to water's cohesive and adhesive properties. Water molecules are attracted to each other because of hydrogen bonding, a phenomenon known as cohesion, which allows the water to form a dome-like shape above the rim before it overflows. This cohesive force is what makes a film of water form and resist spilling out immediately, as you might have observed when adding a few extra drops to an already full glass.
Regarding the ice melting in a glass of water, the ice displaces an amount of water equal to its own weight. Since ice is less dense than water, it displaces a larger volume while floating. Upon melting, the ice turns into water that takes up less volume than the water it had displaced. Therefore, the water level remains the same, and it does not spill over the glass's brim when the ice melts.