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Sand is being dumped from a conveyor belt at a rate of 20 cubic ft/min into a pile the shape of an inverted come whose diameter and height are always the same.

(a) Find the rate of increase of the height when the pile is 10ft high.

This is a 2 part problem. Please show me how to do the first part and I will be able to do the second part. Thanks

  • Calculus - ,

    Just use the volume formula

    v = 1/3 pi r^2 h

    Since diameter = height = 2r
    r = h/2

    v = pi/3 * (h/2)^2 * h
    v = pi/12 h^3

    dv/dt = pi/4 h^2 dh/dt

    20 = pi/4 (10) dh/dt

    dh/dt = 8/pi

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