It's been ages since I took chemistry, but here's my take, for what it's worth.

The critical question is, when heated to liquid form, will the ice cube take up more than 2/3 its previous volume? To phrase it another way, would 2 cubic centimeters of water (to pick a random value) produce at least 3 cubic centimeters of ice when frozen? Does water expand in volume by 150% or more when frozen to ice?

If so -- if water in its solid state takes up at least 150% of its volume in its liquid state, then when the ice cube melts, the water won't spill over the top of the beaker, because the 2/3 of the ice cube that was submerged took up more volume than the entire ice cube when melted into water.

If water expands by less than 150% when frozen to ice, then when the ice cube melts the water wil overflow the beaker, because the melted ice won't fit into the volume displaced by the 2/3 of the ice cube that was underwater.

Of course, there's surface tension, so the water might not *necessarily* overflow the beaker, and I don't know how to account for the loss of water into the air as vapor, like you mentioned. If your impression is that this is meant to be a straightforward and simple question, then I wouldn't worry about those extra factors. If you're fairly certain that your teacher wants you to factor them in, then I don't know how to help you with that -- sorry!

Iss "blinded me with Science" achar