Question

The area $A$ of a circle is related to its radius by the equation
$A=\pi r^2$. The change in area with respect to the radius is $x\times \pi$ $m$. When the radius is $5m$, find the value of $x$.

Answer 1

The (instantaneous) rate of change of the area with respect to the radius is
$\frac{dA}{dr}=2\pi r$

When $r=5m,$
the area is changing at the rate of =$\left(\pi \right)10=10\pi m^2/m$

$\therefore x=10$