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A cone-shaped tank, point down, 10 feet tall with a 5-foot top radius. Water pours in at a steady 2 cubic feet per minute. How fast is the water level rising when it's 6 feet deep?
The ladder in episode 21 had one equation and two variables, so differentiating got you straight to the answer. The cone has three variables: volume, radius, height, and one equation, V = ⅓πr²h. Differentiate it as it stands and the product rule gives you two unknown rates in one equation, a dead end.
The fix is geometry. The water is always a smaller cone with the same shape as the tank.
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2026/10/05
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