Question

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

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

Answer 1

Answer: (B)

$12\pi$

Answer 2

The correct answer is B:$12\pi$
The area of a circle $(A)$ with radius $(r)$ is given by,
$A=πr^2$
Therefore, the rate of change of the area with respect to its radius $r$ is
$\frac{dA}{dr}=\frac{d}{dr}(πr^2)=2πr$
∴When $r = 6 cm$,
$\frac{dA}{dr}=2π\times6=12πcm^2/s$
Hence, the required rate of change of the area of a circle is $12π cm^2 /s$. The correct answer is B.