A circular fountain in a park is represented on the coordinate plane by the equation…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
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.
(i) Express the surface area of the water as a definite integral with proper limits.
(ii) Evaluate the integral obtained in part (i) to determine the exact area of the water surface.
(iii) Using π≈3.14, calculate the area correct to two decimal places.