Optimization question calculus : zoom in.

detailed explanation so i can properly understand

So hmm check the picture below, that's the silo, notice the top of the cylinder is inside with grain... and the bottom, well, that's the (base no included)

so











now, I'd like to point out, we also get critical points from the denominator being zero, so 3r²=0, gives us r=0, which is a critical point, however, with a radius of 0, well, there's no volume, so, the is not feasible for the phenomena, so is not applicable, though is a valid critical point

critical points from the denominator being zero, are usually asymptotic or "cusps", the function reaches an extrema, however the tangent is not horizontal and thus is not differentiable at that point, even though is an extrema.

The answer is