Somehow I think I copied my class notes incorrectly...

As part of Rate of Change:
At a sand and gravel plant, sand is faling off a conveyor and onto a conical pile at a rate of 10 cubic ft. per min. The diameter of the base of the cone is approximately 3 times the altitude. At what rate is the height of the pile changing when the pile is 15 ft high?

Question

Somehow I think I copied my class notes incorrectly...

As part of Rate of Change:
At a sand and gravel plant, sand is faling off a conveyor and onto a conical pile at a rate of 10 cubic ft. per min. The diameter of the base of the cone is approximately 3 times the altitude. At what rate is the height of the pile changing when the pile is 15 ft high?

anonymous · Answer

I don't think I was copying it correctly...I'm confused at what I was doing.
$$V = (1/3) \Pi r^2h $$

dh/dt = ? when h=15

diameter = 3 * (altitude)
2r = 3h
r = (3/2)h

$$V = (1/3) \pi ((3/2)h^2)h $$
$$V = (3/4)\pi h^3 $$

$$dV/dt = (9/4)\pi h^2 (dh/dt)$$

$$10 = (9/4) \pi (15)^2 (dh//dt)$$
 
= $$(8/405) \pi ft/\min.$$

anonymous · Answer

That is a lot. What in particular are you confused about?