A stone is dropped into a quiet lake and waves move in a circle at a speed of 3.5 cm/sec. At the instant when the radius of the circular wave is 7.5 cm, how fast is the enclosed area increasing?

Explanation

given that, `(dr)/(dt) = 4` cm/s

`r= 10`cm

`A= pi r^2`

`(dA)/dt = (d pi r^2)/dt = pi (dr^2)/(dt)`

` = pi (d r^2)/(dr) (dr)/(dt)`

`= pi (2r)(4)`

`=2 pi 10* 4 cm^2`/s

`=80 pi cm^2`/sec

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