Sand is falling onto a cone-shaped pile at the rate of 9pi cubic feet per minute. the diameter of the base is always 3 times the height of the cone. At what rate is the height of the pile changing when the pile is 12 feet high.(adsbygoogle = window.adsbygoogle || []).push({});

work:

dV/dt=+9 ft^3/min

d=3h then r=3h/2 dr/dt=(3/2) dH/dt

Find dH/dt when h=12 ft. which means r=18 ft

V=pi(r)^2h/3

dV/dt=(pi/3)(r^2*dh/dt+h*2r*(3/2)dH/dt)

9pi ft^3/min=(pi/3)(r^2*dh/dt+h*2r*(3/2)dH/dt)

would this be the correct way to find the answer and get dH/dt i get 27/792 ft/min is this correct?

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# Related rates and sand

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