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Question
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?
Solution
Let us assume that radius of the circle = r.
Given `(dr)/dt = 5` cm/s
Area of a circle A `= pir^2`
Rate of change of A with respect to t, `(dA)/(di) = 2pi r (dr)/dt`
`= 2 pi r (5)`
`= 10 pi r`
r = 8 cm
`therefore (dA)/dt = 10 pi (8)`
= 80π cm2/sec.
=> Rate of increase of enclosed area 80π cm2/sec.
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