Question

The rate of change of area of a circle with respect to its radius, when its radius is $1\text{cm}$ is _____

Answer 1

Area of a circle $\left(A\right)=\pi r^2$
Rate of change of area with respect to its radius is given by,
$\frac{dA}{dr}=2\pi r$
At $r=1,\frac{dA}{dr}=2\pi \times 1$
$\therefore \frac{dA}{dr}=2\pi {\text{cm}}^2/\text{cm}$