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calculus

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Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the pile is 20 feet high?

  • calculus - ,

    v=1/3*pi*r^2h r=2/h
    V=1/3*pi*(h/2)^2*h
    =1/3*pi*h^2/4*h
    =1/12*pi*h^3

    V'=10ft^3/min
    h=20ft

    V'=1/12*pi*3h^2*h'

    10=1/12*pi*3(20)^2*h'
    solve for h'

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