minimizing metal is simply minimizing surface area.
Area = 2Pir^2+2Pir(h) = (ends plus side)
the volume = 1000 is immaterial if you want to prove h=2r is the best solution
dA/dr = 4Pir + 2Pih
dA/dh = 0 + 2Pir - this implies r = 0. throw this away
4Pir = -2Pih
4r = -2h
in cyclindrical/polar coordinates, a negative radius is the same as a positive radius.