A stone is dropped into a quiet lake. If the waves moves in circles at the rate of 30 cm/sec when the radius is 50 m, the rate of increase of enclosed area, is

# A stone is dropped into a quiet lake. If the waves moves in circles at the rate of 30 cm/sec when the radius is 50 m, the rate of increase of enclosed area, is

1. A

$30\pi {\mathrm{m}}^{2}/\mathrm{sec}$

2. B

$30{\mathrm{m}}^{2}/\mathrm{sec}$

3. C

$3\pi {\mathrm{m}}^{2}/\mathrm{sec}$

4. D

none of these

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### Solution:

Let the radius of the circular wave ring be r cm at any time t.

Then $\frac{dr}{dt}=30\mathrm{cm}/\mathrm{sec}$ (Given)

Let A be the area of the enclosed ring. Then,

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