Question

The area $A$ of a circle is related to its diameter by the equation $A=\frac{\pi }{4}{D}^2$. The change in area with respect to the diameter is $x\times \pi$, when the diameter is $10m$. Find the value of $x$.

Answer 1

The (instantaneous) rate of change of the area with respect to the diameter is
$\frac{dA}{dD}=\frac{\pi }{4}\left(2D\right)=\frac{\pi D}{2}$

Where, $D=10m,$ the area is changing at the rate of $\left(\frac{\pi }{2}\right)10=5\pi m^2/m$