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

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A formula for the volume of a conic section does not exist in a closed form for the described scenario of a partially filled conic tank. To determine the volume of the liquid, one must use a volume integral that accounts for the specific dimensions and shape of the cone. The known parameters include the height of the liquid, the total volume of the cone, the length of the cone, and the base radius. This approach allows for accurate calculation of the liquid's volume within the conic section. Understanding the geometry and applying integral calculus is essential for solving this problem.
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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.
 

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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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