Water is being poured into an empty cylindrical tank. The rate of change of the volume of water in the tank at time t minutes is given by dtdV=10t2−6t (in litres per minute). At t=0, the tank already contains 50 litres of water.
(i) Determine the volume V(t) of water in the tank at any time t.
(ii) Find the volume of water in the tank after 3 minutes.
(iii) At what time t (to the nearest tenth of a minute) will the volume of water reach 200 litres?