WBJEE · Maths · Application of Derivatives
If the rate of increase of the radius of a circle is \(5 \mathrm{~cm} / \mathrm{sec}\), then the rate of increase of its area, when the radius is \(20 \mathrm{~cm}\), will be
- A \(10 \pi\)
- B \(20 \pi\)
- C \(200 \pi\)
- D \(400 \pi\)
Answer & Solution
Correct Answer
(C) \(200 \pi\)
Step-by-step Solution
Detailed explanation
Hints : \(\mathrm{A}=\pi \mathrm{r}^2 \quad \frac{d r}{d t}=5\) \[ \begin{aligned} & \frac{\mathrm{dA}}{\mathrm{dt}}=2 \pi r \frac{\mathrm{dr}}{\mathrm{dt}}=2 \pi 20(5) \\ & =200 \pi \end{aligned} \]
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