If the rate of change of area of a circle is equal

(b) $\frac{1}{\pi}$ unit

Let $r$ be the radius and $A$ be the area of the circle at any time $t$. Then,

$A=\pi r^{2}$

$\Rightarrow A=\frac{\pi D^{2}}{4}$           $\left[\because r=\frac{D}{2}\right]$

$\Rightarrow \frac{d A}{d t}=\frac{\pi D}{2} \frac{d D}{d t}$

$\Rightarrow \frac{d D}{d t}=\frac{\pi D}{2} \frac{d D}{d t}$        $\left[\because \frac{d A}{d t}=\frac{d D}{d t}\right]$

$\Rightarrow \frac{D}{2}=\frac{1}{\pi}$

$\Rightarrow r=\frac{1}{\pi}$ units