Buoyancy of Ice.?

Question

If you put an ice cube in a glass, and fill the glass with water to the very brim. Knowing that water expands when it freezes, when the ice cube melts will any of the water spill of the sides of the glass?
The answer is no. Can anyone figure it out using calculus?

Answer 1

You don't need calculus. You just need to understand buoyancy. It's a matter of volume and mass. If you fill the glass, then how much mass is actually there? The ice will stick up above the water by the amount of volume difference. When the ice melts, the same mass occupies less space. The part that was above the surface of the container is now in the glass. Use the known densities to figure it out. You know also that mass is constant. It's just the density and occupied volume that change.

Answer 2

while water freezes, it expands. This expansion facilitates gasses to fill the voids between the water molecules, starting to be buoyancy. If the ice is floating on best of the water, this implies area of it rather is not in the water. the burden of the quantity of ice is represented in the water, yet no longer the quantity of the ice, because of the fact a factor of it rather is not in the water. (floating above the floor). So the quantity might proceed to be the comparable. Now in case you have been to thoroughly submerge the ice in the water, than the quantity may be slightly much less while the ice melts.

Answer 3

You don't need calculus. Since density is mass over volume, and ice is less dense, then when the ice changes state back to water, it's mass will be the same and its volume will be less.