Question

Find the rate of change of the area of a circle with respect to its radius $r$ when
(i) $r=3$ cm
(ii) $r=4$ cm

• A. $6\pi ,8\pi$
• B. $5\pi ,8\pi$
• C. $4\pi ,10\pi$
• D. $2\pi ,8\pi$

Answer 1

The correct option is A $6\pi ,8\pi$

The area of a circle $\left(A\right)$ with radius $\left(r\right)$ is given by,
$A=\pi r^2$

Now, the rate of change of the area with respect to its radius is given by,

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

At $r=3$ cm,
$\frac{dA}{dr}=2\pi \left(3\right)=6\pi$

At $r=4$ cm,

$\frac{dA}{dr}=2\pi \left(4\right)=8\pi$