Rate water has to be added to Leaking cone

In summary, the conversation discusses a problem involving a leaking inverted conical tank and the rate at which water is being pumped into the tank. Through mathematical equations and relationships, it is determined that the correct answer is found by subtracting 6500 from the equation pi/27(3*200)^2(20).
  • #1
angelcase
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Homework Statement



Water is leaking out of an inverted conical tank at a rate of 6500 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.

Homework Equations



V=1/3 pi(r)^2*h

relationships:

4/2r=6/h
therefore,
r=1/3h


Substituting h for r:
V=1/3 pi (1/3h)^2(h)
V=pi/27(h)^3
V'=dv/dt= pi/27 (3h)^2dh/dt
dv/dt=pi/27 (3*200)^2(20)

since the cone is leaking we have to find:

dv/dt-6500=pi/27(3*200)^2(20)
 
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  • #2
Others may want to confirm, but this looks good to me.
 
  • #3
That answer is incorrect..that is why I posted it...I can't find the correct answer..I was just showing my work so someone could tell me where I went wrong...Does anyone know??

...I got it..I shouldn't have the parenthesis around the 3*200, since only the 200 is squared...
 
Last edited:
  • #4
Yes, that's right. Sorry I missed the error before. A tip for next time: if you know your answer is wrong, let us know and we (or at least I) will look more carefully for an error.
 
  • #5
Thank you..and I will do that.
 

FAQ: Rate water has to be added to Leaking cone

What is the purpose of adding water to a leaking cone?

The purpose of adding water to a leaking cone is to reduce the rate of leakage and prevent further damage to the cone. This can also help maintain the structural integrity of the cone.

How do I determine the rate of water that needs to be added to a leaking cone?

The rate of water that needs to be added to a leaking cone can be determined by conducting a leak test. This involves measuring the amount of water that leaks from the cone over a certain period of time and then adjusting the rate of water added accordingly.

What factors can affect the rate of water that needs to be added to a leaking cone?

The rate of water that needs to be added to a leaking cone can be affected by various factors such as the size and location of the leak, the material of the cone, and the surrounding environment. It is important to consider these factors when determining the appropriate rate of water to add.

Can adding too much water to a leaking cone cause any issues?

Adding too much water to a leaking cone can potentially cause issues such as overflow or structural damage. It is important to carefully monitor the rate of water added and make adjustments as needed to prevent any further damage.

Is there a recommended rate of water that should be added to a leaking cone?

There is no specific recommended rate of water that should be added to a leaking cone as it can vary depending on the factors mentioned previously. It is important to carefully assess the situation and make adjustments accordingly to effectively address the leakage issue.

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