Finding the Volume of a Conic Section: Is There a Formula?

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Homework Help Overview

The discussion centers around finding the volume of a conic section, specifically in the context of a conic-shaped tank partially filled with liquid. The original poster describes the dimensions and orientation of the tank, including the height of the liquid, the volume of the cone, the length of the cone, and the base radius.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster seeks to determine if a specific formula exists for calculating the volume of liquid in the conic tank based on the provided parameters. Some participants question the feasibility of a closed-form solution for this geometry and suggest the use of volume integrals instead.

Discussion Status

The discussion is ongoing, with participants exploring the nature of the problem and the potential methods for finding the volume. There is an acknowledgment that a closed-form formula may not exist, leading to the suggestion of using integrals.

Contextual Notes

Participants note the challenge posed by the geometry of the conic section and the implications of the tank's orientation on the calculations. The original poster's attempt to illustrate the problem visually was hindered by formatting issues, which may affect clarity in communication.

jasbo11166
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I would like to know if an equation exists for the volume of a section of a cone. For example, a conic shaped tank lying on its side with the point to the left and the circular base to the right is filled partially with liquid. The height of the liquid, volume of the cone, length of the cone and the base radius of the cone are known.

* ----------
* * |
* * |
* * |
* * R
* __________* ____ | __ liquid level
* * | |
* * h |
* ----------
|-------- H ---------|

How would you find the volume of the liquid in the tank?

Thank you,

Jim
 
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I appologize, but when the message was posted it removed all the spaces in the drawing I made. I hope you will be able to provide an answer with the text description.

Thanks,

Jim
 
See attached image for a graphical view of the problem.
 

Attachments

There is no closed form formula for this geometry, you will need to use a volumn integral over the region of interest.
 

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