Question

The rate of change of the area (in ${\text{cm}}^2/s$) of a circle with respect to its radius $r$ at $r=6\text{cm}$ is

• A. $8\pi$
• B. $11\pi$
• C. $12\pi$
• D. $10\pi$

Answer 1

The correct option is C $12\pi$

Area of circle,

$A=\pi r^2$

Differentiating w.r.t. $r$, we get

$\Rightarrow \frac{dA}{dr}=\frac{d}{dr}\left(\pi r^2\right)$

$\Rightarrow \frac{dA}{dr}=\pi \frac{d}{dr}\left(r^2\right)$

$\Rightarrow \frac{dA}{dr}=2\pi r$

When $r=6$, we get

$\Rightarrow \frac{dA}{dr}=12\pi {\text{cm}}^2/s$

Hence, Correct answer is $\left(B\right)$