Discussion
If the rate of increase of the radius of circle 5 cm/sec, then the rate of increase of its area when the radius is 20 cms, will be
Answer: D
The area increases at \(200\pi\) cm2/sec.
With \(A = \pi r^{2}\), differentiate with respect to time:
\[ \begin{aligned} \frac{dA}{dt} &= 2\pi r\frac{dr}{dt} \\ &= 2\pi \times 20 \times 5 = 200\pi \end{aligned} \]
\(100\pi\) forgets the factor 2 from differentiating \(r^{2}\), and \(400\pi\) is \(\pi r^{2}\) itself at \(r = 20\), the area rather than its rate of change.
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