How to finde the volumen between 2 Cylinders?

[Polymerman]

Hallo,

I would like to ask for your experience. I need to find the volume with triple integrals between 2 cylinders. They are not along the same axis.

To imagine how they are found, they form a cross, like this: +

The first one is an ordinary cylinder and it follows the form z= 3 sin (phi). This was really easy.

The second one is an elliptic cylinder. Here are starting the problems. The area of this second cylinder is given by x^2/a^2+y^2/b^2. For a = 2.6 and b= 3.0

But I just can transform this second one into cylindric coordinates and at the same time turn it 90° from the first cylinder to form this "+" cross.

Do you have any idea?

Thanks a lot!

Best regards.

[Polymerman]

Here is a basic MAthCAD document... it is missing the main part =S

[Fred_Kohlhepp]

Is this what you mean about two cylinders?

If so, then we can move forward to develop the integral

[Polymerman]

Hi Fred

You´ve got it! Wow, yes it is like that. How would you start the integral?

Due to a some reason, I can not see the graphs...

Thanks y lot!

[RichardJ]

Right click on the graph and uncheck "border". Depending on your OS, that might fix it.

[Polymerman]

Hi Richard,

it fixed it!

Thanks!

It is getting more and more exiting. Now, how can be the volume found? It looks like you have the answer is almost there.

[Polymerman]

Hi Fred,

I have solved the problem in another way. But I am very interested in the way you are solving the problem. I would like to ask you if you could continue with it? It was really sophisticated and I would really like to see your answer.

Here is my version as well.

Thanks!

[Fred_Kohlhepp · Accepted solution]

The trick to the integration is to set the limits correctly.

I wouldn't bet lunch that this was right.

[MikeArmstrong]

I wouldn't bet lunch that this was right.

I wouldn't bet my lunch on anything

Mike

[Polymerman]

Thanks Fred,

I wouldn't bet my lunch as well... Sorry for not answering before. My Hard disk just died.

I think it is quite well, numerical approaches give a little smaller value, but it is ok. I need to learn more about MathCAD to fully understand that what you did.

Regards and thank all of you for helping.

[VladimirN]

Hello!

Hope this helps: https://www.math.drexel.edu/~jwd25/Calc4_Winter_09/lectures/Lecture8B.pdf

[Polymerman]

Thanks Vladimir,

it was quite helpful, however, the definition of the function is still not perfect...