TS EAMCET · Maths · Application of Derivatives
If water is poured into a cylindrical tank of radius 3.5 ft at the rate of \(1 \mathrm{cu} \mathrm{f} / \mathrm{min}\), then the rate at which the level of the water in the tank increases (in \(\mathrm{f} / \mathrm{min}\) ) is
- A \(\frac{1}{154}\)
- B \(\frac{8}{77}\)
- C \(\frac{2}{77}\)
- D \(\frac{1}{11}\)
Answer & Solution
Correct Answer
(B) \(\frac{8}{77}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} V & =\pi r^2 h ; \frac{d V}{d t}=\pi r^2 \frac{d h}{d t} \\ \Rightarrow 1 & =\pi \times 3.5^2 \frac{d h}{d t} \Rightarrow \frac{d h}{d i}=\frac{7}{22} \times \frac{2 \times 2}{7 \times 7}=\frac{2}{77}\end{aligned}\)
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