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12th grade

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Wheat is falling from a chute onto a level floor at a rate of 8pi ft3/min to form a conical pile. If the height of the pile is always equal to the radius of its base, at what rate is the radius increasing when the pile is 8 ft deep?

  • 12th grade -

    V = (1/3)πr^2h
    but h=r
    V= (1/3)πr^3
    dV/dt = πr^2 dr/dt
    so when h = 8 , r = 8 and dV/dt = 8π

    8π = π(8)^2 dr/dt
    dr/dt = 8π/(64π) = 1/8 ft/min

  • 12th grade -

    THANKS!

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