Calculus

Sand falls from a conveyor belt at the rate of 20 m^3/min. The sand forms a conical pile where the height of the cone is always 4 times the radius. How fast is the radius changing when the pile is 4 meters high?

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  1. volume of cone
    = V = (1/3)π r^2 h, but we know h = 4r or r = h/4
    V = (1/3)π (h^2/16)(h)
    = (1/48)π h^3

    dV = (1/16)π r^2 dr/dt
    when h = 4, r = 1
    20 = (1/16)π(1) dr/dt
    dr/dt = 320/π m/min

    check my arithmetic, did it on the screen instead of writing it out first

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