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Question 5:
A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s. At the instant when the radius of the circular wave 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) with respect to time (t) is given by,
[By chain rule]
It is given that
.
Thus, when r = 8 cm,
Hence, when the radius of the circular wave is 8 cm, the enclosed area is increasing at the rate of 80π cm2/s.
