A tank, as shown in the figure below, formed using a combination of a cylinder and a cone, offers better drainage as compared to a flat bottomed tank. 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 $2 \text{ cm}^3/\text{s}$. The semi-vertical angle of the conical tank is $45^\circ$. 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 $\text{r} = 2\sqrt{2} \text{ cm}$. (iii) (a) Find the rate at which the wet surface of the conical tank is decreasing at an instant when radius $\text{r} = 2\sqrt{2} \text{ cm}$. OR (iii) (b) Find the rate of change of height 'h' at an instant when slant height is $4 \text{ cm}$.