A stone is dropped into a lake and waves move in circles at a speed of 8 cm/sec. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing?

$160 \pi cm^2/sec$

The correct answer is Option (4) - $160 \pi cm^2/sec$

r → radius

$\frac{dr}{dt}=8cm\sec$

$A=\pi r^2$

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$ so $\left.\frac{dA}{dt}\right]_{r=10}=2\pi×10×8$

$=160 \pi cm^2/sec$