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Hello, I posted a question earlier but now I'm stuck on the second part of the question. Please help me.

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

Find the rate of increase of the radius when the pile is 20 ft. high.


  • Calculus - ,

    As we saw earlier,

    v = 1/3 pi r^2 h

    Since diameter = height = 2r
    h = 2r

    v = pi/3 * r^2 * 2r
    v = 2pi/3 r^3

    dv/dt = 2pi r^2 dr/dt
    20 = 2pi (10)^2 dr/dt
    dr/dt = 1/(10pi)

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