A circular metal plate of radius 21cm is cut into six congruent sectors of equal area.
(i) Find the central angle of each sector.
(ii) Calculate the area of one such sector, leaving π in your answer.
(iii) One sector is left unused. It is melted and recast into a rectangular sheet whose breadth is 5cm. Determine the length of this rectangle.
(iv) State ONE assumption made in part (iii) that is necessary for your calculation to be valid.