Question

What is the rate of change of the area of a circle with respect to its radius $r$ at $r=6$ $cm$.

• A. $12\pi$ $cm$
• B. $16\pi$ $cm$
• C. $18\pi$ $cm$
• D. $24\pi$ $cm$

Answer 1

Answer: (A)

$12\pi$ $cm$

Given, $r=6$ $cm$

Area of a circle with radius $r$ is, $A=\pi r^2$
$\Rightarrow \frac{dA}{dr}=2\pi r$

At $r=6cm$,

$\frac{dA}{dr}=2\pi \left(6\right)=12\pi cm$