AP EAMCET · Maths · Application of Derivatives
If a cylindrical vessel of given volume \(V\) with no lid on the top is to be made from a sheet of metal, then the radius \((r)\) and height \((h)\) of the vessel so that the metal sheet used is minimum, is
- A \(r=\sqrt[3]{\frac{\pi}{V}}, h=\sqrt[3]{\frac{\pi}{V}}\)
- B \(r=\sqrt{\pi V}, h=\sqrt{\pi V}\)
- C \(r=\sqrt[3]{\frac{V}{\pi}}, h=\sqrt[3]{\frac{V}{\pi}}\)
- D \(r=\sqrt{\frac{V}{\pi}}, h=\sqrt{\frac{V}{\pi}}\)
Answer & Solution
Correct Answer
(C) \(r=\sqrt[3]{\frac{V}{\pi}}, h=\sqrt[3]{\frac{V}{\pi}}\)
Step-by-step Solution
Detailed explanation
We have given, \(V=\) volume of cylindrical vessel \(r=\) radius and \(h=\) height As we know for cylindrical vessel \[ v=\pi r^2 h \] Let \(S\) be the area of metal sheet used to form a cylindrical vessel. Then,…
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