1) A blacksmith has a rectangular sheet of Iron.He has to make a cylindrical vessel both circular ends are closed. When he minimise the wastage of the sheet of iron, then what is the ratio of the wastage to the utilized area of sheet?

You have not specified the initial size of rectangle or the dimensions of the cylinder or whether all surfaces of the cylinder are uniform or not or whether the closed cylinder is welded shut or folded shut or glued shut. So it is not possible to give a specific answer.
Theoretically, the wastage can be brought very to zero if you can manage to form the sheet