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Question: A stone is dropped into a quiet lake and waves move in a circle at a speed of 4 cm/s. At the instant...

A stone is dropped into a quiet lake and waves move in a circle at a speed of 4 cm/s. At the instant when the radius of the circular wave is 10 cm, the enclosed area increases at the rate :

A

100p cm2/s

B

80p cm/s

C

40 cm2/s

D

None of these

Answer

None of these

Explanation

Solution

drdt\frac{dr}{dt} = 4cm/sec

when r = 4cm, A = pr2

dAdt\frac{dA}{dt} = p.2rdrdt\frac{dr}{dt} = p . 2 × 4 × 4 = 32p cm2/sec