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How can I find the surface area of the portion of a sphere (given as x^2+y^2+z^2 = 3*c^2) that is within the paraboloid 2c*z = x^2+y^2?
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Here is a graph showing the upper half of the sphere (in red) and the paraboloid (in black) in the case when c = 2. How can I find the surface area of the portion of the red sphere that is within the paraboloid?
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