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Home » Surprise Rule: Eating Before an MRI Could Ruin Your Test—Learn It Now! - Leaselab

Surprise Rule: Eating Before an MRI Could Ruin Your Test—Learn It Now! - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 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}

📌 Given \( \frac{dV}{dt} = -3 \) m³/min and \( h = 6 \):

📌 = \frac{\pi}{9} (6)^2 \frac{dh}{dt} = \frac{\pi}{9} \times 36 \times \frac{dh}{dt} = 4\pi \frac{dh}{dt}

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