[1]Volume of the cone

[2]Area of the curved surface.

Solve [1] for r and plug in this term into [2]:

Now differentiate a wrt h (V is a constant!). You'll get:

Solve a'(h) = 0 for h. This is obviously only possible if

Solve for h. Substitute V by the term of [1] and solve for h again. You'll get

Remark: Especially the differentiation of a is really horrible. So I hope for you that someone knows a simpler, shorter way to solve the question.