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are back in college? :| or you are taking a very weird job interview…
Just write down the equation to calculate the volume
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Neither. Surprising structures in reality are beautiful. *Why* is this the case? An equation is a poor explanation here.
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Scale so height is 1. Consider sweeping through horizontal slices z = h in [0, 1]. Ratio of radii /
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as function of height is sqrt(h), so ratio of disk areas is h, average ratio over [0,1] gives 1/2.
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Elaborating more intuitively: the radii grow more slowly as h increases, but volume increases faster as r increases!
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And: those two rates of change are precisely inverse in this case! Gorgeous.
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