Roundabouts are often made on busy roads to ease the traffic and avoid red lights.One such round-about is made such that equation representing its boundary is given by $C_1 : x^2 + y^2 = 64$. There is a circular pond with a fountain in the middle of the roundabout whose equation is given by $C_2 : x^2 + y^2 = 4$.
Based on the given information, answer the following questions :
(i) Represent the given equations $C_1$ and $C_2$ with the help of a diagram. [1 mark]
(ii) Express y as a function of $x$, ($y = f(x)$), for both $C_1$ an $C_2$. [1 mark]
(iii) (a) Using integration find the area of region covered by the roundabout. [2 marks]
OR
(iii) (b) Using integration, find the area of region covered by circular pond. [2 marks]