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kevinr
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[SOLVED] Rate of Change - Just checking
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.
v = [tex](1/3)\pi r^2[/tex]
r' = h' / 2 (i think this is right - not sure)
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!
Homework Statement
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.
Homework Equations
v = [tex](1/3)\pi r^2[/tex]
r' = h' / 2 (i think this is right - not sure)
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!