SOLUTION: please help, me with this calculus homework about related rates Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a p

Algebra ->  Functions -> SOLUTION: please help, me with this calculus homework about related rates Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a p      Log On


   

Question 1156175: please help, me with this calculus homework about related rates
Gravel is being dumped from a conveyor belt at a rate of 35 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (Round your answer to two decimal places.)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) What are we supposed to find? rate of change of height: dh/dt

(2) What are we given? rate of change of volume: dV/dt

So to solve the problem, we need to get the relationship between volume V and height h.

V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29

That gives us the volume in terms of r and h; so we need to get r in terms of h.

The problem tells us d=h. d = 2r; so r = (1/2)d = (1/2)h.

Substitute in the volume formula:

V+=+%281%2F3%29%28pi%29%28%281%2F2%29h%29%5E2%28h%29+=+%281%2F12%29%28pi%29%28h%5E3%29

Now you are ready to take the derivative and solve the problem.

dV%2Fdt+=+%28%281%2F12%29%28pi%29%283h%5E2%29%29%28dh%2Fdt%29

Plug in h=10 and the given value of dV/dt to solve for dh/dt....