# Math Help - Differentiation Word Problem

1. ## Differentiation Word Problem

This problem is killing me, any help would be greatly appreciated

Sand is falling off a conveyor belt onto a conical pile at the rate of 15 cubic feet per minute. The diameter of the base of the cone is approx twice the height. At what rate is the height of the cone changing when it is 10 feet high?

2. Originally Posted by CrEpE
This problem is killing me, any help would be greatly appreciated

Sand is falling off a conveyor belt onto a conical pile at the rate of 15 cubic feet per minute. The diameter of the base of the cone is approx twice the height. At what rate is the height of the cone changing when it is 10 feet high?
1) What is the volume of a cone?

2) Since the diameter is twice the radius and the diameter is twice the height, in what way can we relate the radius of the conical tank and the height of the conical tank?

If you can answer both of these questions, you will be able to come up with a volume equation that is dependent only on the height.

From that point, differentiate V with respect to h and then evaluate it when $\frac{\,dV}{\,dt}=15$ cubic feet/min and when $h=10$ feet.

Does this make sense? Can you take it from here?

3. Sorta. The equation comes out to V=(1/3)Pi(H)^3. The part I get stuck at is the differentiation.

Almost positive I did this wrong, but the answer I got was .047.

4. Originally Posted by CrEpE
Sorta. The equation comes out to V=(1/3)Pi(H)^3. The part I get stuck at is the differentiation.

Almost positive I did this wrong, but the answer I got was .047.
Note I made a typo in my original post, I meant to say $\frac{\,dV}{\,dt}$, not $\frac{\,dh}{\,dt}$.