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March 27, 2017

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At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 9 pi cubic inches per minute. If the height is always 3 times the radius, find the rate of change of the radius at that instant.

  • AP calculus AB - ,

    dV/dt = 9 = surface area * dh/dt

    9 = (pi r^2)(dh/dt)
    but
    h = 3 r
    so
    dh/dt = 3 dr/dt
    so
    9 = (pi r^2)(2 dr/dt)
    but r = 3
    so
    9 = 9 pi (2 dr/dt
    dr/dt = 1/2pi

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