KCET · Maths · Application of Derivatives
The rate of change of area of a circle with respect to its radius \( r=2 \mathrm{cms} \) is
- A \( 04 \)
- B \( 2 \pi \)
- C \( 12 \)
- D \( 4 \pi \)
Answer & Solution
Correct Answer
(D) \( 4 \pi \)
Step-by-step Solution
Detailed explanation
We know that, area of circle is given by
\[
A=\Pi r^{2}
\]
\[
\text { So, } \frac{d A}{d r}=2 \Pi r
\]
At \( r=2 \mathrm{~cm} \), we have \( \left(\frac{d A}{d r}\right)_{r=2}=4 \Pi \)
\[
A=\Pi r^{2}
\]
\[
\text { So, } \frac{d A}{d r}=2 \Pi r
\]
At \( r=2 \mathrm{~cm} \), we have \( \left(\frac{d A}{d r}\right)_{r=2}=4 \Pi \)
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