TS EAMCET · Maths · Application of Derivatives
A vessel in the shape of an inverted cone of height \(10 \mathrm{ft}\) and semi vertical angle \(30^{\circ}\) is full of water. Due to a hole at the vertex, the slant height of the water in the vessel is decreasing at a constant rate of \(\frac{1}{\sqrt{3}}\) feet per minute. The rate (in cu. feet \(/ \mathrm{min}\) ) at which the volume of water in the vessel is decreasing, when the volume of water is \(\frac{8 \pi}{\sqrt{3}}\) cubic feet, is
- A \(\frac{2 \pi}{\sqrt{3}}\)
- B \(2 \pi\)
- C \(2 \pi \sqrt{3}\)
- D \(\pi \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(2 \pi\)
Step-by-step Solution
Detailed explanation
Given height of cone \(=10 {ft}\) vertical angle \(=30^{\circ}\)…
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