An open-top water tank is in the shape of a cuboid. The tank has a square base of side length s m, and has a volume of 216 m^3. Find expressions, in terms of s, for:

a) the height of the tank.
b) the surface area of the tank

Given that the surface area of the open-top water tank is minimised:
c) find the value of s.
(looking for clear workouts and reasoning / explanation behind every step taken no matter how basic it may be)
Answers:
a) h = 216/s^2
b) A = s^2 + 864
c) s = cube root of 432