TS EAMCET · Maths · Application of Derivatives
The height of a right circular cylinder is decreasing while is diameter is increasing at a rate of \(4 \mathrm{~cm} / \mathrm{see}\) so as to keep its volume unchanged. the rate of change in its lateral surface area (in \(\mathrm{cm}^2 / \mathrm{sec}\) ) at the instant when its diameter is \(8 \mathrm{~cm}\) and height is \(12 \mathrm{~cm}\), is
- A \(24 \pi\)
- B \(-24 \pi\)
- C \(48 \pi\)
- D \(-48 \pi\)
Answer & Solution
Correct Answer
(C) \(48 \pi\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{d(2 r)}{d t}=4 \mathrm{~cm} / \mathrm{s}\) \(\Rightarrow \quad \frac{d r}{d t}=2 \mathrm{~cm} / \mathrm{s}\) Volume of cylinder \(=\pi r^2 h\)…
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