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calculus word problem

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a conveyor belt pours gravel into a pile at a rate of 20 lbs per minue. the pile is shaped like an upside-down cone. the proportions of the cone are such that when the pile is complete, the diameter of the base is 6 ft and the height is 10 feet. how fast is the height of the pile changing when the pile is 7 ft high?

I keep getting stuck!

  • calculus word problem - ,

    let the radius be r and the height be h
    Assuming the cone maintains the same shape

    2πr=6
    r = 3/π

    and r/h = (3/π)/10
    r = 3h/(10π)

    V = (1/3)πr^2 h
    = (1/3)π(9h^2/(100π^2))h
    = 3h^3/(100π)

    dV/dt = (9/100π)h^2 dh/dt

    At this point you will have to know what the relationship between lbs of concrete and cubic feet is, I work in metric and no longer know those units.

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