Question

The radius of a circle is increasing at the rates of $0.7$ cm/sec. What is the rate of increasing of its circumference, when the radius of the circle is $4.9$ cm ?

Answer 1

$\text{Given}\frac{dr}{dt}=0.7cm/sec\text{Perimeter}P=2\pi r\text{, where}r=\text{radius}\frac{dP}{dt}=\frac{d}{dt}\left(2\pi r\right)\Rightarrow \frac{dP}{dt}=2\pi \frac{dr}{dt}$

$\frac{dP}{dt}=2\pi \frac{\left(0.7\right)cm}{\sec }\frac{dP}{dt}=\frac{7}{5}\pi cm/sec$

it does not depend on radius of circle