I ran across this problem when working on an architecture design project. I know this probably involves integral math but I'm not very familiar with it. Any help would be appreciated.
2026-03-27 17:52:21.1774633941
How to cut a sphere in 3 parts of equal volume?
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If you would like to cut off a spherical cap with $1/3$ the volume of a sphere, let the radius of the sphere be $r$ and the height of the cap be $h$. The volume of the cap is $V=\frac {\pi h^2}3(3r-h)$ To have this $1/3$ of the sphere we need $$\frac 49\pi r^3=\frac {\pi h^2}3(3r-h)\\4r^3=9rh^2-3h^3$$ Alpha doesn't find a neat solution, but $\frac hr \approx 0.77393$ so cut a cap with height about $3/4$ of the radius off each side and you will have equal volume in each piece.