Engine displacement is the measure of the cylinder volume swept by all the pistons of a piston engine. The piston moves inside the cylinder bore The cylinder bore in the form of circular cylinder open at the top is to be made from a metal sheet of area $75\mathit{\pi }{\mathrm{cm}}^2$.
Based on the above information, answer the following questions :
(i) If the radius of cylinder is $\mathrm{r}\mathrm{cm}$ and height is $\mathrm{h}\mathrm{cm}$, then write the volume $\mathrm{V}$ of cylinder in terms of radius $\mathrm{r}$.
(ii) Find $\frac{\mathit{d}\mathit{V}}{\mathit{d}\mathit{r}}$.
(iii) (a) Find the radius of cylinder when its volume is maximum.
OR
(b) For maximum volume, $\mathit{h}>\mathit{r}$. State true or false and justify.