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Home » Total beds: 18 × 3 = 54 - Dachbleche24

Total beds: 18 × 3 = 54 - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A conical tank with height 12 meters and base radius 4 meters is being drained at a rate of 3 m³/min. How fast is the water level decreasing when the water is 6 meters deep?

📌 V = \frac{1}{3}\pi r^2 h

📌 By similar triangles, \( \frac{r}{h} = \frac{4}{12} = \frac{1}{3} \), so \( r = \frac{h}{3} \).

📌 Substitute into volume:

📌 V = \frac{1}{3}\pi \left(\frac{h}{3}\right)^2 h = \frac{1}{3}\pi \frac{h^3}{9} = \frac{\pi}{27} h^3

📌 Differentiate with respect to time:

📌 \frac{dV}{dt} = \frac{\pi}{27} \cdot 3h^2 \frac{dh}{dt} = \frac{\pi}{9} h^2 \frac{dh}{dt}

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