Question

The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant

Answer 1

Answer: $2\ \text{units}$

Step-by-step explanation:

Given

Rate of increase in area of the circle is numerically equal to twice the rate of increase to twice the rate of increase in its circumference.

It can be written as

$\Rightarrow \dfrac{d(\pi r^2)}{dt}=2\times \dfrac{(2\pi r)}{dt}\\\\\Rightarrow 2\pi r\dfrac{dr}{dt}=4\pi \dfrac{dr}{dt}\\\\\Rightarrow r=2\ \text{units}$