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Given these constructions, there is no maximal volume. The volume approaches infinity as the angle approaches 90 degrees.

In fact these formulae are unrelated

the lateral height of a cone is the length of a line segment from the apex of the cone along its side to its base.

try harder.

I’m a math grad student I don’t deserve to be humiliated like this

sorry, it was either you or me :V

I think? But I’m only at undergrad level in mathematics, so feel free to point out if I f@*$ed up. I was never particularly amazing at geometry.

this is entirely correct; very thorough too :3

also this should entirely be accessible to anyone who’s done just enough calculus to talk about maxima and minima of continuously differentiable functions, which means either high school or undergrad calc, depending on your educational path; don’t be so worried ;p

(incidentally you could have skipped from h=l/√3 straight to the answer by using arccos instead of arctan but arctan is a nicer function anyways so w/e)

me looking at this post