Posted by **jhon** on Saturday, May 5, 2012 at 3:09am.

Water is leaking out of an inverted conical tank at a rate of 12200 cubic centimeters per minute at the same time that water is being pumped into the tank at a constant rate. The tank has height 15 meters and the diameter at the top is 6.5 meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 1.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

- calculus(related rates) -
**Steve**, Saturday, May 5, 2012 at 10:53am
You know, when you posted this earlier, with a typo, my solution should have enabled you to get the corrected answer. I assume you did that, and are now just confirming your subsequent work.

.

.

.

Right?

when the water is at depth y, the radius r of the surface can be found using similar triangles:

r/y = (6.5/2)/15

r = 13/60 y

at depth y, the volume of water is

v = 1/3 pi r^2 y

= 1/3 pi (13/60)^2 y^3

= 169pi/10800 y^3

dv/dt = -12200+C = 169pi/3600 y^2 dy/dt

at y=1m=100cm, dy/dt = 21cm/min

-12200 + C = 169pi/3600 * 10000 * 21 =

C = 30971

## Answer this Question

## Related Questions

- calcalus - Water is leaking out of an inverted conical tank at a rate of 12200 ...
- Calculus - Water is leaking out of an inverted conical tank at a rate of cubic ...
- Calculus (pleas help!!!) - Water is leaking out of an inverted conical tank at a...
- calculus - please help! - Water is leaking out of an inverted conical tank at a ...
- Calculus - Water is leaking out of an inverted conical tank at a rate of 1100.0 ...
- Calculus - Water is leaking out of an inverted conical tank at a rate of 1100.0...
- calculus - Water is leaking out of an inverted conical tank at a rate of 60000 ...
- calc rates - Water is leaking out of an inverted conical tank at a rate of 10600...
- calculus - Water is leaking out of an inverted conical tank at a rate of 1100 ...
- calculus - Water is leaking out of an inverted conical tank at a rate of 1600.0 ...