calculus

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Gravel is being dumped from a conveyor belt at a rate of 50 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 12 feet high?
Hint: The volume of a right circular cone with height and radius of the base is given by V=(1/3)(pi)(r^2)(h).

  • calculus -

    V=(1/3)(pi)(r^2)(h).
    But we are told that 2r=h or r = h/2
    then
    V=(1/3)(pi)(h^2/4)(h).
    =(1/12)pi(h^3)

    dV/dh = (1/4)pi(h^2)dh/dt
    when h = 12, and dV/dt = 50
    50 = (1/4)pi(144)dh/dt
    dh/dt = 200/(144pi) = 25pi/18 ft/min

  • calculus -

    this is wrong

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