SOLUTION: Water is flowing into a conical reservoir 25.0 m deep and 10.0 m across the top, at a rate of 16.0 m3/min. How fast is the surface rising when the water is 10.0 m deep?
Algebra ->
Test
-> SOLUTION: Water is flowing into a conical reservoir 25.0 m deep and 10.0 m across the top, at a rate of 16.0 m3/min. How fast is the surface rising when the water is 10.0 m deep?
Log On
Question 1074453: Water is flowing into a conical reservoir 25.0 m deep and 10.0 m across the top, at a rate of 16.0 m3/min. How fast is the surface rising when the water is 10.0 m deep? Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Water is flowing into a conical reservoir 25.0 m deep and 10.0 m across the top, at a rate of 16.0 m3/min. How fast is the surface rising when the water is 10.0 m deep?
-----------
Assuming 10 m is the diameter, r = 5
---
Vol = pi*r^2*h/3
Find r in terms of h:
For 0 <= h <= 25,
r/h = 5/25
r = h/5
---
---
dVol/dt = pi*h^2/25*dh/dt = 16
dh/dt = 400/(pi*h^2)
At h = 10,
dh/dt = 4/pi meters/minute
