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A container in the form of a right circular cone (vertex down) has a radius of 4m and height of 16m. If water is poured into the container at the constant rate of 16m^3/min, how fast is the water level rising when the water is 8m deep.

  • Calculus -

    easy way:
    r = (4/16) h = (1/4) h
    surface area = pi r^2
    = pi (1/16) h^2
    dV = surface area * dh
    dV = pi (1/16) h^2 dh
    DV/dt = (1/16) pi h^2 dh/dt

    hard way:
    V = (pi/3) r^2 h given
    again r^2 = (1/16) h^2
    V = (pi/3)(1/16) h^3
    dV/dh = (pi/16) h^2
    again dV/dt = (pi/16) h^2 dh/dt

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