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Home » Time for second part: \(\frac20040 = 5\) hours. - Dyverse

Time for second part: \(\frac20040 = 5\) hours. - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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V = \frac{1}{3}\pi r^2 h
By similar triangles, \( \frac{r}{h} = \frac{4}{12} = \frac{1}{3} \),...
Substitute into volume:
V = \frac{1}{3}\pi \left(\frac{h}{3}\right)^2 h = \frac{1}{3}\pi \frac...
Differentiate with respect to time:
\frac{dV}{dt} = \frac{\pi}{27} \cdot 3h^2 \frac{dh}{dt} = \frac{\pi}{9...
Given \( \frac{dV}{dt} = -3 \) m³/min and \( h = 6 \):
= \frac{\pi}{9} (6)^2 \frac{dh}{dt} = \frac{\pi}{9} \times 36 \times \...
Solve:
\frac{dh}{dt} = \frac{-3}{4\pi} \approx -0.239 \text{ m/min}

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