Find the dimensions of the right circular cylinder with top

Find the dimensions of the right circular cylinder (with top and bottom) of volume V0 which has the smallest surface area.

V0 = pi r^2h h = V0/pi r^2 S = 2pi rh + pi r^2 S = 2pi r(V0/pi r^2) + pi r^2 S = 2V0/r + pi r^2 dS/dr = -2V0/r^2 + 2pi r = 0 2[-V0/r^2 + pir] = 0 -V0/r^2 = pir r^3 = V0/pi r = (V0/pi)^1/3..........(1) h = V0/pir^2 h = Vo/pi(Vo/pi)^2/3 h = (V0/pi)^1/3...(2)