If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to

A
$\frac{2}{π} unit$
B
$\frac{1}{π} unit$
C
$\frac{π}{2} units$
D
$π units$

Solution:

Let $x$ be the diameter and $A$ be the area of a circle.

Then,

$\begin{array}{l} A = \frac{π}{4} x^{2} \\ \Rightarrow \frac{d A}{d t} = \frac{π}{2} x \frac{d x}{d t} \end{array}$

$\Rightarrow \frac{d x}{d t} = \frac{π x}{2} \frac{d x}{d t}$ $[∵ \frac{d A}{d t} = \frac{d x}{d t} (given)]$

$\Rightarrow x = \frac{2}{π}$

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