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Let's say I have one spherical cap, resulting from cutting a sphere centered at origin and with radius R1 with a plane, whose normal goes into the direction of the x axis. The spherical cap can be seen as a body with two surfaces, a planar surface and a spherical surface with total area equal to S1. Now I have a second sphere, centered at another arbitrary point and with radius R2. In the cases in which the spherical cap and the second sphere overlap, dividing the spherical face of the cap into two parts with resulting values for the partial spherical surfaces S1a and S1b, how can one calculate analytically S1a and S1b?

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The question is not clear. What does it mean, to calculate a surface? Are you trying to calculate an area? a volume? something else? –  Gerry Myerson Oct 6 '11 at 12:07
    
clarified, thanks for the correction –  flow Oct 6 '11 at 12:16

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