Posted by **Lizzy** on Sunday, October 7, 2012 at 10:29pm.

A water tank has the shape of an inverted right circular cone whose base radius is equal to half its height. Water is being pumped in at 2 cubic meters per second. How fast is the water rising when the water is 3 meters deep?

- Calculus - free body diagram -
**Reiny**, Sunday, October 7, 2012 at 10:49pm
radius = (1/2)h

r = (1/2)h

r = h/2

V = (1/3)πr^2 h

= (1/3)π(h^2/4)h

= (1/12)πh^3

dV/dt = (1/4)πh^2 dh/dt

when h = 3, dV/dt = 2

2 = (1/4)π(9) dh/dt

dh/dt = 8/(9π) m/s

Check my calculations, I did not write them out first.

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