An agricultural research centre builds a cubic underground storage chamber with a volume of \(12167\ m^3\).
(i) Evaluate the length of the inner side of the cubic water tank using the prime fatorization method.
(ii) Evaluate the area of the base of the tank.
(iii) The inner walls (excluding the top cover) and the floor of the tank need to be tiled. Evaluate the total area to be tiled.
(iv) If area of a square water collection platform is \(2500\ m^2\). The platform is extended, increasing its area to \(3600\ m^2\). Find the increase in the side length of the platform.