U = 2·h + r·(pi + 2) --> h = (U - r·(pi + 2))/2
A = 2·h·r + pi·r^2/2
A = 2·((U - r·(pi + 2))/2)·r + pi·r^2/2
A = r·U - r^2·(pi + 4)/2
A' = u - r·(pi + 4) = 0 --> r = U / (pi + 4)
h = (U - r·(pi + 2))/2 = (U - (U / (pi + 4))·(pi + 2))/2 = U / (pi + 4) = r
Die Höhe sollte so groß gewählt werden wie der Radius
A = (U / (pi + 4))·U - (U / (pi + 4))^2·(pi + 4)/2 = U^2 / (2·(pi + 4))
Einsetzen
A = U^2 / (2·(pi + 4)) = 20^2 / (2·(pi + 4)) = 28.00 m²
Die Fläche beträgt maximal ca. 28 m².