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?


closed as unclear what you're asking by astralfenix, manshu, Marius, Deusovi, bleh Apr 30 '16 at 14:50

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    $\begingroup$ I think this question relates to fluid dynamics. So science tag might be applicable. $\endgroup$ – manshu Apr 30 '16 at 12:13
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    $\begingroup$ Are your half-spheres some kind of ideal ones of negligible buoyancy and thickness? $\endgroup$ – Jonathan Allan Apr 30 '16 at 12:19
  • $\begingroup$ By half-sphere, do you mean hemisphere? $\endgroup$ – manshu Apr 30 '16 at 12:20
  • $\begingroup$ Could you clarify which things are A and B in the ratio A/B that you are after? The first and last bowl volumes, or a fixed ratio as we progress? $\endgroup$ – Jonathan Allan Apr 30 '16 at 12:33
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    $\begingroup$ I can't see how this question can make sense, so I'm voting to close. 1) It depends on the bowl material and thickness 2) If we're talking about a stack of bowls balanced on top of eachother, getting smaller and smaller by some constant ratio, then clearly the max ratio is infinite (assuming the thickness decreases by the same ratio). If the thickness is constant, then you can't have an infinitely high stack as implied by the question. Did he mean to say minimum ratio? Then it depends on the material bouyancy/thickness. $\endgroup$ – astralfenix Apr 30 '16 at 13:00

I say



"The bowls are mathematical ideal ones with no thickness, who have nonetheless the property the if you put a half sphere in the water, the water rises to half the volume of the half sphere."


As soon as you place the second bowl of any positive volume into the first, the water in the previously full first bowl will rise and hence spill.

OK this is now not true due to the edit made by the OP specifying that the bowls are half filled.


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