A circular fountain in a park is represented on the coordinate plane by the equation x2+y2=16 (all lengths in metres). Water occupies only the portion of the fountain that lies in the first quadrant.
a. (i) Express the surface area of the water as a definite integral with proper limits.
b. (ii) Evaluate the integral obtained in part (i) to determine the exact area of the water surface.
c. (iii) Using π≈3.14, calculate the area correct to two decimal places.