The Total solution for NCERT class 6-12
A stone is dropped into a quiet lake and waves move incircles at the speed of 5 cm/s. At the instant when the radius of the circularwave is 8 cm, how fast is the enclosed area increasing?
The area of a circle (A)with radius (r)is given by
Therefore, the rate of change of area (A) withrespect to time (t) isgiven by,
[By chain rule]
Thus, when r = 8 cm,
Hence, when the radius of the circular waveis 8 cm, the enclosed area is increasing at the rate of 80π cm2/s.