COMEDK · Maths · 27. Application of Derivatives
Oil from a conical funnel is dripping at the rate of \(5 \mathrm{~cm}^3 / \mathrm{s}\). If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top is
- A \(-\dfrac{4}{45 \pi} \mathrm{~cm} / \mathrm{s}\)
- B \(-\dfrac{2 \pi}{45} \mathrm{~cm} / \mathrm{s}\)
- C \(-\dfrac{4 \pi}{45} \mathrm{~cm} / \mathrm{s}\)
- D \(\dfrac{8}{45 \pi} \mathrm{~cm} / \mathrm{s}\)
Answer & Solution
Correct Answer
(A) \(-\dfrac{4}{45 \pi} \mathrm{~cm} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
Let \(R = 10\) cm be the radius and \(H = 20\) cm be the height of the conical funnel. Let \(r\) and \(h\) be the radius and height of the oil level at any time \(t\). By similar triangles, \(\dfrac{r}{h} = \dfrac{R}{H} = \dfrac{10}{20} = \dfrac{1}{2}\), so \(r = \dfrac{h}{2}\).…
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