(adsbygoogle = window.adsbygoogle || []).push({}); [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 = [tex](1/3)\pi r^2[/tex]

r' = h' / 2 (i think this is right - not sure)

3. The attempt at a solution

So i got

v' = [tex](1/3)\pi (2rr'h + r^2h')[/tex]

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' = [tex](1/3)\pi (2r(h'/2)h + r^2h')[/tex] ->

r = 1

h = 2

SO:

v' = [tex](1/3)\pi (2h' + h')[/tex] ->

h' = [tex]5/\pi[/tex]

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

Thanks!

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# Homework Help: Rate of Change - Just checking

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