I have a half sphere half filled with water. The sphere is made of some infinitely thin material with a mass per unit area so that as I fill the bowl and put it in water it just floats (no water is leaking in the bowl).
I put this bowl (half sphere) on a table (with something under it to keep it from falling) and put another bowl (the bowls have always the same properties) in the water.
Now I put another bowl filled half with water in this bowl, after wich I put in the last one again a bowl half filled with water in it, and again, and again....
Now it is clear that if I put a second bowl in the first the has a ratio of volumes B/A=0.9, and the water spoils over. On the other hand, if I put a second (and third, fourth...etc.) bowl in that has a ratio B/A=0.1, so if we go down from 0.9 to 0.1, there comes a point that the water just not spills over. For what ratio of B/A this happens?