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So the problem that I'm trying to solve is as follows:

Assume 1/8 of a sphere with radius $r$ whose center is at the origin (for example the 1/8 which is in $R^{+}$). Now two parallel planes are intersecting with this portion where their distance is $h$ (Note:$h$ < $r$) and one of the planes passes through the origin.What is the area cut off by these two planes on the 1/8 of the sphere? You may assume anything that you think is required to calculate this area, as given, my suggestion would be the angles at which the parallel planes cross xyz planes.

Obviously I'm not interested in trivial cases for example when the plane which passes through origin is one of xy, xz or zy planes.

I hope I explained everything clearly. I wish I could draw a picture for this but I don't how. Let me know if you need more clarification. Any hint or help about how to find this area is highly appreciated.

enter image description here

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    It would help avoid misunderstanding if the problem stated that the surface area can be anywhere from 0 to some positive value and that it clearly is a function of 2(?) angles (obviously in addition to h) which define the planes' exact orientation. Or state that the 1/8 circle is defined to the (+,+,+) section of the (x,y,z) coordinate space. By saying that it is 1/8 but leaving it up in the air as to its precise location, it's too easy to assume we are talking about 2 planes slicing a whole circle and then taking 1/8 of that somehow. It would also help to clarify that the sphere has radius r.2011-05-20
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    It is actually stated in the problem that as an example you can assume the 1/8 sphere which is in $R^{+}$ so it is defined in (+,+,+), although this does not have any effect on the final answer.2011-05-20
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    I have also stated that I'm not interested in trivial cases so all the situation you have mentioned, are just trivial cases which needs no calculation. But I agree with you abut the case where h>=r I wanted to mention that somehow but I thought that would be clear, I'll change that in the problem.2011-05-20
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    @Jose_X: please do not use answers to make comments.2011-05-20

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