question_answer

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

Answer:

Let r be the radius of circle at any time t.     Then,    \[\frac{dr}{dt}=0\cdot 7\,\,\text{cm/s}\] Now, let C denotes the circumference of circle. Then,             \[C=2\pi r\] \[\Rightarrow \] \[\frac{dC}{dt}=2\pi \frac{dr}{dt}\] \[\Rightarrow \] \[\frac{dC}{dt}=2\pi (0.7)=1.4\pi \,cm/s\] Hence, the rate of increase of its circumference is\[1.4\pi \,cm/s\],