The problem states: sand falls onto a conical pile at a gravel yard at a rare of 10 cubic feet per minute. The base of the pile is approximately three times the altitude. How fast is the pile getting taller when the pile is 15 feet tall?(adsbygoogle = window.adsbygoogle || []).push({});

Volume = πr² h/3

dV = 10 h = 15

dt

When I use implicit differentiation, I get

d [V] = π/3(r²dh/dt + 2rh dr/dt)

dt

solving for dh/dt I get dV/dt(3/πr² - 2rh dr/dt

The answer they give is 8/405πm however, without knowing what the dr/dt is, I'm not sure how to solve this. The closest I cpme is 8/15π, bur r=t this is without a quantity for dr/dt.

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# Rate of change: Height of a conical pile

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