A large industrial water tank is such that, when the depth of the water in the tank is \(x\) metres, the volume \(V\text{ m}^3\) of water in the tank is given by \(V=243-\frac13(9-x)^3\). Water is being pumped into the tank at a constant rate of \(3.6\text{ m}^3\) per hour.

Find the rate of increase of the depth of the water when the depth is 4 m, giving your answer in cm per minute. [5]