U(r)= 45/r - π·r/2 + 2·r = 45·r^{-1} - π·r/2 + 2·r
U'(r) = -45·r^{-2} - π/2 + 2 = -45/r^2 - π/2 + 2 = 0
Hier nur mal eine Lösung zum anschließenden Vergleich
A = 2·r·h + 1/2·pi·r^2 --> h = (2·A - pi·r^2)/(4·r)
U = 2·r + 2·h + pi·r = 2·r + 2·(2·A - pi·r^2)/(4·r) + pi·r = (2·A + r^2·(pi + 4))/(2·r)
U' = (r^2·(pi + 4) - 2·A)/(2·r^2) = 0 → r = √(2·A/(pi + 4))
h = (2·A - pi·√(2·A/(pi + 4))^2)/(4·√(2·A/(pi + 4))) = √(2·A/(pi + 4))