2D shell integrating over a 3D ball, orange/intersection = dS

So I want to integrate this blue surface from R-r to R+r (over the red ball) but I have trouble defining the surface element.

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    $\begingroup$ I don't think you explained the problem well. What exactly is the question? Not what you are doing, but what the problem asks you to do. $\endgroup$ – Andrei Feb 23 at 16:39
  • $\begingroup$ There's no specific problem. I just want to know how to find this particular intersection element. If it makes it easier you can think of it as finding the volume of the red ball. $\endgroup$ – John Feb 23 at 16:45
  • $\begingroup$ How the intersection is relevant? Integrate from R to R+r and multiply by 2. $\endgroup$ – Moti Feb 24 at 5:19

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