Solve a Challenging Ellipsoid Problem Today!

  • Thread starter Hadhod
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In summary, the conversation is about developing a formula for the volume of an ellipsoid using parametrization and triple integration. The conversation also touches on finding the limits of integration and the use of solid of revolution by integration. The conversation ends with a reminder to chat through private messages to avoid warnings from forum administrators.
  • #1
Hadhod
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Challenging Problems


Develop a formula for the volume of an ellipsoid of the form
x2\a2 +y2\b2 +z2\c2 = 1



pls Help me;
I need the answer today
 
Last edited:
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  • #2
You can parametrise it as follows:
http://en.wikipedia.org/wiki/Ellipsoid

Then perform a triple integration to find the volume in spherical coordinates. But the problem I got with this method is finding the limits of integration for p.
 
  • #3
Thank you very much Defennnder

but I don't understand it .
 
  • #4
What exactly don't you understand? Are you familiar with using triple integrals in order to find the volume of some three-dimensional region?
 
  • #5
I want to underatand
how I can develop a formula for the volume of an ellipsoid by that equation
 
  • #6
If you have no idea how to find a volume of rotation, why are you attempting a problem like this?
 
  • #7
Thank you HallsofIvy for helping me
 
  • #8
So

there is no one can help me ?^-*
 
  • #9
Since you refuse to help yourself--
 
  • #10
Does the method of volume by rotation work if all three semi-axes are unequal?
 
  • #11
it must be equal
 
  • #12
Do you mean to say all are equal? Or 2 are equal? Because if all are equal, then you have a sphere. If only 2 are equal then you only need to find the volume by rotation by integration as Halls said.
 
Last edited:
  • #13
I am sorry
2 are equal
 
  • #15
Thank you alooooooooooooooooooooooooooooooooot
 
  • #16
ya
I am from UoS
Why??
whze this??
 
  • #17
Um just a reminder before the two of you get warnings from forum admins. Please do all your chatting through Private Messages.
 
  • #18
Ohhhhh
 

1. What is an ellipsoid problem?

An ellipsoid problem is a mathematical problem that involves finding the solution to an equation involving an ellipsoid, which is a three-dimensional geometric shape resembling a stretched sphere. These problems can involve finding the volume, surface area, or other properties of an ellipsoid.

2. Why are ellipsoid problems considered challenging?

Ellipsoid problems are considered challenging because they often involve complex mathematical equations and require advanced problem-solving skills. Additionally, ellipsoids have many different properties and parameters that can make finding a solution more difficult.

3. How can solving an ellipsoid problem benefit scientific research?

Solving an ellipsoid problem can provide valuable insights and information in various fields of science, such as physics, engineering, and geology. The solutions to these problems can help in understanding the behavior and properties of ellipsoids in real-world applications.

4. What are some common techniques used to solve ellipsoid problems?

Some common techniques used to solve ellipsoid problems include integration, differential equations, and numerical methods such as Monte Carlo simulation. Additionally, computer software and programs can also be used to solve these problems efficiently and accurately.

5. Are there any real-world applications of ellipsoid problems?

Yes, there are many real-world applications of ellipsoid problems, including calculating the orbits of satellites, optimizing the shape of lenses in optics, and predicting the behavior of atoms and molecules in quantum mechanics. Ellipsoid problems also have practical applications in fields such as geodesy, geophysics, and statistics.

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