Question

A stone is dropped into a quite lake and waves moves in circles spreading out radially at the speed of 0.2m/s. At the instant when the radius of the circular wave is 4 p m, how fast is the enclosed area increasing ? (1) 4 m2 / s p (2) 1.6 m2 / s (3) 2m2 / s (4) 1 2 / 2 m

Answer 1

Answer:

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Answer 2

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We know that the area of a circle with radius “r” is given by A = πr2.

Hence, the rate of change of area “A’ with respect to the time “t” is given by:

dA/dt = (d/dt) πr2

By using the chain rule, we get:

(d/dr)(πr2). (dr/dt) = 2πr.(dr/dt)

It is given that, dr/dt = 4 cm/sec

Therefore, when r = 10 cm,

dA/dt = 2π. (10). (4)

dA.dt = 80 π

Hence,

when r = 10 cm, the enclosing area is increasing at a rate of 80π cm2/sec

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