AP EAMCET · Maths · Application of Derivatives
A container is the shape of an inverted cone. Its height is \(6 \mathrm{~m}\) and radius is \(4 \mathrm{~m}\) at the top. If it is filled with water at the rate of \(3 \mathrm{~m}^3 / \mathrm{min}\) then the rate of change of height of water (in \(\mathrm{mt} / \mathrm{min}\) ) when the water level is \(3 \mathrm{~m}\), is
- A \(\frac{3}{4 \pi}\)
- B \(\frac{2}{9 \pi}\)
- C \(16 \pi\)
- D \(2 \pi\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{4 \pi}\)
Step-by-step Solution
Detailed explanation
Let \(V\) be the volume, \(r\) be the radius and \(h\) be the height of an inverted cone at any time \(t\). Then Given, \(\frac{d v}{d t}=3 \mathrm{~m}^3 / \mathrm{min}\) We know that, From similarity of triangle…
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