Two sectors belong to the same circle. The lengths of their arcs are in the ratio 5 : 8.
a. Show that the central angles of the two sectors are also in the ratio 5 : 8.
b. Explain why the areas of the two sectors are in the ratio 5 : 8.
c. Would the result in part (ii) necessarily hold if the two sectors came from different circles with different radii? Give a brief reason for your answer.