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Sand is falling into a cone whose height is always 1/2 the diameter of the base. If the sand is falling at a rate of 1/2 cubic meters per min. How fast is the height increasin when the pile is 3 meters high?

so far i've drawn my diagram and got this far.

h = 1/2 the base
dv/dt = +1/2m3/min


the equation i was going to use is
V = 1/12pih3

then i get

dv/dt = (1/2pi)(3h2)dh/dt

i dont know how to get the h?
any help?


Homework Helper
Gold Member
You're asked to find dh/dt when the height is 3 h=3:wink:

But there is a problem with your starting equation V = (1/12)pih3....If the height is always half the diameter, then r=4h not h/4
ok, that was stupid of me,
i dont even know why i was having trouble with that now >.<

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