Water is being poured at the rate of 27 m\(^3\)/sec into a cylindrical vessel of base radius 3 m. Find the rate at which the water level is rising.

Q.21 Water is being poured at the rate of 27 m\(^3\)/sec into a cylindrical vessel of base radius 3 m. Find the rate at which the water level is rising.

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(\frac{3}{\pi}\) m/sec

Let \(h\) be the height of water at time \(t\). Volume \(V = \pi r^2 h = \pi(3)^2h = 9\pi h\).

\(\frac{dV}{dt} = 9\pi\frac{dh}{dt}\). Given \(\frac{dV}{dt} = 27\): \(27 = 9\pi\frac{dh}{dt}\), so \(\frac{dh}{dt} = \frac{3}{\pi}\) m/sec.

The water level is rising at \(\frac{3}{\pi}\) m/sec.

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Water is being poured at the rate of 27 m\(^3\)/sec into a cylindrical vessel of base radius 3 m. Find the rate at which the water level is rising.

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