# Rate of Change - Just checking

1. Dec 3, 2007

### kevinr

[SOLVED] Rate of Change - Just checking

1. The problem statement, all variables and given/known data

Sand is poured into a conical pile with the height of the pile equaling the diameter of the pile. If the sand is poured at a constant rate of 5m^3/s at what rate is the height of the pile increasing when height is 2 meters.

2. Relevant equations

v = $$(1/3)\pi r^2$$
r' = h' / 2 (i think this is right - not sure)

3. The attempt at a solution

So i got
v' = $$(1/3)\pi (2rr'h + r^2h')$$

So i have 2 unknowns r' and h'. Since we can make the connection that r' = h'/2 i replace that in the equation and get:

v' = $$(1/3)\pi (2r(h'/2)h + r^2h')$$ ->

r = 1
h = 2

SO:

v' = $$(1/3)\pi (2h' + h')$$ ->
h' = $$5/\pi$$

Im not sure if this answer is right but if you can please check over my work, i would appreciate it.

Thanks!

2. Dec 3, 2007

### HallsofIvy

Staff Emeritus
It would have been better to have clearly stated somewhere that v'= 5, but it's obvious that you did use that. Yes, that is the correct answer.

3. Dec 3, 2007

### kevinr

Sorry i thought it was in the problem question i posted.

Well thanks!