Calculating the Speed of a Sand Pile's Height Increase

[superjen]

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.

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

Needs:
dh/dt

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

then i get

dv/dt = (1/2pi)(3h²)dh/dt

i don't know how to get the h?
any help?

 

[gabbagabbahey]

You're asked to find dh/dt when the height is 3 meters...so h=3

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

 

[superjen]

ok, that was stupid of me,
i don't even know why i was having trouble with that now >.<