I am currently learning about volumes of revolution in calulus, and have looked ahead to surfaces of revolution as well. I want to try and extend this concept to revolving 3d functions over the x-axis into the fourth dimension. I found this thread:(adsbygoogle = window.adsbygoogle || []).push({});

https://www.physicsforums.com/showthread.php?t=64536

and saw how to find the content of a 3-ball (5th post).

I attemted to use this idea to find the content of the revolution about the x-axis of the revolution about the x-axis of 4-x^{2}but I couldn't quite puzzle through the method described in the above thread for anything other than spheres. The closest I came was the surface area of the solid of revolution, and realizing that I need to describe the circumference of the 3d solid of revolution with respect to the radius and/or height (for a sphere of radius 1 it would be 2[itex]\pi[/itex]ssin(r))

Can anyone point me in the right direction, or does this seem way too far past a Calculus DC student in highschool? (and if so I'm still really interested in how this would work)

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# Help extending volumes of revolution to fourth dimension

Can you offer guidance or do you also need help?

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