by Bill Graham

Answer to Ice Spheres from Vol 1, No. 3

I wish Archimedes were here to help with this one.

TUB 1: The solid ice sphere displaces its own mass of water and, when melted, will exactly fill the that amount. The level does not change.
TUB 2: If you crack the hollow sphere open, then the air inside and outside of the sphere will mingle without changing the mass or the water level. As the sphere melts, it acts just like the one in the first sphere.
TUB 3: Cracking the sphere enclosing a vacuum would allow air to get into the hollow and increase the total mass of the sphere thus causing the tub to overflow.
TUB 4: Cracking the sphere enclosing a helium would allow the helium to escape and be replaced by heavier air causing the tub to overflow.
TUB 5: Replacing the iron ball with air will make the sphere lighter so that it floats up and causes the water level to drop. Once the sphere melts enough so that the iron ball drops to the bottom of the tub, this is what will happen.
Do you agree?