Question

A stone is dropped into a quiet lake and waves moves in circles at a speed of $3cm/s$. At the instant, when the radius of the circular wave is $10cm$, then the rate at which its perimeter is increasing is

• A. $6\pi \text{cm/s}$
• B. $9\pi \text{cm/s}$
• C. $1.5\pi \text{cm/s}$
• D. $3\pi \text{cm/s}$

Answer 1

The correct option is A $6\pi \text{cm/s}$

Perimeter of the circle
$P=2\pi r\Rightarrow \frac{dP}{dt}=2\pi \frac{dr}{dt}$
We know that $\frac{dr}{dt}=3\text{cm/s}$
So, $\frac{dP}{dt}=6\pi \text{cm/s}$