Question

If the radius of a circle is \(r = 6\) cm, then the rate of change of Area with respect to radius is:

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

Hint:

Differentiate A=πr² to get dA/dr=2πr, then plug in r=6.

Answer 1

The Correct Option is B

Step 1: Think of it as a small-change approximation:
If the radius grows by a tiny amount $dr$, the area grows by roughly a thin ring of circumference $2\pi r$ and width $dr$, so $dA \approx 2\pi r\, dr$, giving $dA/dr = 2\pi r$.

Step 2: Plug in the given radius:
At $r = 6$, $dA/dr = 2\pi(6) = 12\pi$.

Final Answer:
The required rate is $12\pi$ sq cm per cm. \[ \boxed{12\pi} \]