Posted by **ali** on Wednesday, May 2, 2012 at 12:52pm.

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 65 meters. If the water level is rising at a rate of 21 centimeters per minute when the height of the water is 10 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute

- calcalus -
**Steve**, Wednesday, May 2, 2012 at 2:52pm
when the water is at depth y, the radius r of the surface can be found using similar triangles:

r/y = (65/2)/15

r = 13/6 y

at depth y, the volume of water is

v = 1/3 pi r^2 y

= 1/3 pi (13/6)^2 y^3

= 169pi/108 y^3

dv/dt = -12200+C = 169pi/36 y^2 dy/dt

at y=10m=1000cm, dy/dt = 21cm/min

-12200 + C = 169pi/36 * 1000000 * 21 = 309708675

C = 309696475

## Answer This Question

## Related Questions

- calculus(related rates) - 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 cubic ...
- Math-Calc - Water is leaking out of an inverted conical tank at a rate of 14000....
- math - Water is leaking out of an inverted conical tank at a rate of 10600.0 cm3...
- math - Water is leaking out of an inverted conical tank at a rate of 11400 cm^3/...
- Calculus (pleas help!!!) - Water is leaking out of an inverted conical tank at a...
- calc rates - Water is leaking out of an inverted conical tank at a rate of 10600...
- Engineering Calc. - Water is leaking out of an inverted conical tank at a rate ...
- 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 ...

More Related Questions