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AP calculus AB

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Water pours out of a conical tank of height 10 feet and radius 4 feet at a rate of 10 cubic feet per minute. How fast is the water level changing when it is 5 feet high?

  • AP calculus AB -

    All three of your questions are pretty much the same idea.

    change in volume = surface area * change in width of slice.

    the surface area = pi r^2
    r at five feet = half of radius at 10 feet so r = 2 feet

    Area = pi r^2 = 4 pi ft^2
    so
    change in volume = (4 pi)(change in height)
    so
    change in volume/time = 4 pi (change in height/time)
    so
    10 ft^3/min = 4 pi ft^2 (dh/dt)
    so
    dh/dt = (10/4pi) ft/min

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