Volume of intersection of non-concentric cylinder and sphere

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I want to calculate volume of intersection of a sphere and cylinder but they are not concentric. Sphere has a radius of 1 and located at (0,0,R+h). Cylinder has a radius of R and centered at origin. I know there is some way to use integration but don't know how to proceed.




calculus




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  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Jul 26 at 0:01










  • Giving us the center and radius of your cylinder does not specify it uniquely. Which way is it oriented?
    – G Tony Jacobs
    Jul 26 at 2:19










  • My mistake. The cylinder has the equation x^2+z^2=R^2
    – Anupam Mishra
    Jul 27 at 21:40














up vote
0
down vote

favorite












I want to calculate volume of intersection of a sphere and cylinder but they are not concentric. Sphere has a radius of 1 and located at (0,0,R+h). Cylinder has a radius of R and centered at origin. I know there is some way to use integration but don't know how to proceed.




calculus




share|cite|improve this question



















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Jul 26 at 0:01










  • Giving us the center and radius of your cylinder does not specify it uniquely. Which way is it oriented?
    – G Tony Jacobs
    Jul 26 at 2:19










  • My mistake. The cylinder has the equation x^2+z^2=R^2
    – Anupam Mishra
    Jul 27 at 21:40












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I want to calculate volume of intersection of a sphere and cylinder but they are not concentric. Sphere has a radius of 1 and located at (0,0,R+h). Cylinder has a radius of R and centered at origin. I know there is some way to use integration but don't know how to proceed.




calculus




share|cite|improve this question











I want to calculate volume of intersection of a sphere and cylinder but they are not concentric. Sphere has a radius of 1 and located at (0,0,R+h). Cylinder has a radius of R and centered at origin. I know there is some way to use integration but don't know how to proceed.





calculus





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 25 at 23:58









Anupam Mishra

1




1











  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Jul 26 at 0:01










  • Giving us the center and radius of your cylinder does not specify it uniquely. Which way is it oriented?
    – G Tony Jacobs
    Jul 26 at 2:19










  • My mistake. The cylinder has the equation x^2+z^2=R^2
    – Anupam Mishra
    Jul 27 at 21:40
















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Jul 26 at 0:01










  • Giving us the center and radius of your cylinder does not specify it uniquely. Which way is it oriented?
    – G Tony Jacobs
    Jul 26 at 2:19










  • My mistake. The cylinder has the equation x^2+z^2=R^2
    – Anupam Mishra
    Jul 27 at 21:40















Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 26 at 0:01




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 26 at 0:01












Giving us the center and radius of your cylinder does not specify it uniquely. Which way is it oriented?
– G Tony Jacobs
Jul 26 at 2:19




Giving us the center and radius of your cylinder does not specify it uniquely. Which way is it oriented?
– G Tony Jacobs
Jul 26 at 2:19












My mistake. The cylinder has the equation x^2+z^2=R^2
– Anupam Mishra
Jul 27 at 21:40




My mistake. The cylinder has the equation x^2+z^2=R^2
– Anupam Mishra
Jul 27 at 21:40















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