Question

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

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

Answer 1

The correct option is B $12\pi$

The area $\left(A\right)$ of circle with radius $r$ is, $A=\pi r^2$
Thus rate of change of area of circle with radius is,
$\Rightarrow \frac{dA}{dr}=2\pi r$.
Hence at $r=6$ cm $,\frac{dA}{dr}=12\pi$ cm