We are given dh/dt=8, h/4=r, we want dV/dt when h=50.2. Sand pouring from a chute forms a conical pile whose height is always equal to twice the diameter. If the height increases at a constant rate of 8 feet per minute what rate is the sand pouring from the chute when the pile is 50 feet high.
Volume of cone is
Using our sub, r=h/4:
Now, it is in terms of h alone. We are given dh/dt.
Now, by using our givens:
That's stacking up pretty fast. But, then again, the pile is growing 8 feet per minute, so dV/dt would have to be high.