GATE 2024 MN – Question 44

Engineering Mathematics · Calculus · 2 marks · Numerical answer

Water enters the inverted conical tank at 300 m³/hour. The tank is 10 m across at the top and 15 m high as shown. Find water-level rise rate in m/min when depth is 5 m, to two decimals.

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Correct answer: 0.50 to 0.60

Explanation

Flow is 5 m³/min. Similar triangles give r/h=5/15=1/3. Thus V=πh³/27 and dV/dh=πh²/9. At h=5, dh/dt=5×9/(25π)=0.57296 m/min, or 0.57.

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