Allgemeine Lösung
V = pi·r2·h --> h = V/(pi·r2)
A(r, h) = 8·r2 + 2·pi·r·h
A(r) = 8·r2 + 2·pi·r·(V/(pi·r2))
A(r) = 8·r2 + 2·V/r
A'(r) = 16·r - 2·V/r2 = 0 --> r = 1/2·V1/3
h = V/(pi·r2) = V/(pi·(1/2·V1/3)2) = 4/pi·V1/3
Einsetzen und ausrechnen
r = 1/2·(1000)1/3 = 5 cm
h = 4/pi·(1000)1/3 = 12.73 cm