Question

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

• A. $30\pi m^2/sec$
• B. $30m^2/sec$
• C. $3\pi m^2/sec$
• D. none of these

Answer 1

The correct option is A $30\pi m^2/sec$

Given, $\frac{dr}{dt}=30cm/sec=0.3m/sec,r=50m$
Area of circle $=\pi r^2$
$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
$\Rightarrow \frac{dA}{dt}=30\pi m^2/sec$