A rectangular metal stand is to be placed on the flat roof of a school building to carry a water tank. The empty stand has a mass of 50kg and the tank, when filled, has a mass of 200kg. The roof can safely bear a pressure of at most 4.0×103Pa.
(i) Calculate the total downward force exerted on the roof by the stand and the filled tank.
(ii) Determine the minimum area the base of the stand must have so that the pressure on the roof does not exceed the safe limit.
(iii) If the base of the stand is made square, find the least length of one side of the square base that satisfies the requirement obtained in part (ii).