Ap Calculus help?

The volume of a certain cone for which the sum of its radius, r, and height is constant is given by V=13πr2(10−r). The rate of change of the radius of the cone with respect to time is 6. In terms of r, what is the rate of change of the volume of the cone with respect to time?

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  • V = (1/3) * pi * r^2 * (10 - r)

    I'm sure that's what you meant

    dr/dt = 6

    V = (1/3) * pi * (10r^2 - r^3)

    dV/dt = (1/3) * pi * (20r * dr/dt - 3r^2 * dr/dt)

    dV/dt = (1/3) * pi * (20r * 6 - 3 * r^2 * 6)

    dV/dt = (6/3) * pi * (20r - 3r^2)

    dV/dt = 2pi * (20r - 3r^2)

    dV/dt = 40pi * r - 6pi * r^2

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