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Recently I baked a spherical cake (3cm radius) and invited over a few friends, 6 of them, for dinner. When done with main course, I thought of serving this spherical cake and to avoid uninvited disagreements over the size of the shares, I took my egg slicer with equally spaced wedges(and designed to cut 6 slices at a go; my slicer has 5 wedges spaced at 1 cm apart) and placed my spherical cake right in the exact middle of it before pressing uniformly upon the slicer. Was I successful in avoiding the feuds over the shares. If so then what could be the mathematical explanation of it and if not then why not? My Setup looked a bit similar like given in the image below:

slicer

Bobson Dugnutt
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  • Could you explain a bit more about the setup, preferably with a drawing? – An.Ditlev Sep 14 '16 at 09:38
  • @An.Ditlev : I do not know if its agood idea but I included this image similar to the setup of mine. –  Sep 14 '16 at 09:56
  • Look up the volume of a spherical cap in Wikipedia. You want each slice to be $1/6$ of the total volume. Find the height of a cap that gives this and the height that gives $1/3$. Those heights plus the center are what you want. – Ross Millikan Sep 14 '16 at 14:43
  • Please see the question I posted after this one http://math.stackexchange.com/questions/1926383/equal-slicing-of-my-spherical-cake –  Sep 14 '16 at 14:54
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    My comment still applies. Your second question just removes the given value of$r$, so the desired locations will scale with $r$ – Ross Millikan Sep 14 '16 at 14:58
  • Yes thanks for the Wikepedia reference.I just looked at it and I see the point. –  Sep 14 '16 at 15:01

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I assume you mean something like this (although this is intended for five persons). If so, then that is obviously not a fair way of dividing the cake (the other slices will be much smaller than the inner slices).

Bobson Dugnutt
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