A tap is connected to such a tank whose conical part is full of water. Water is dripping out from a tap at the bottom at the uniform rate of 2 cm³/s. The semi-vertical angle of the conical tank is 45°.....On the basis of given information, answer the following questions:

(i)Find the volume of water in the tank in terms of its radius r.
(ii)Find rate of change of radius at an instant when r = 2√2 cm
iii) (a) Find the rate at which the wet surface of the conical tank is decreasing at an instant when radius = 2√2 cm
(b) Find the rate of change of height 'h' at an instant when slant height is 4 cm.​