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18. Extra Credit: The surface S is the part of the sphere :02 + y2 + 32 = a2 that lies inside the cylinder 3:4

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18. Extra Credit: The surface S is the part of the sphere :02 + y2 + 32 = a2 that lies inside the cylinder 3:4 + (12(y2 m2) = 0. Sketch it and show that its area equals 20,2(7r 2). HINT: Use cylindrical coordinates and take into account that S is symmetric with respect to both the mz and yzplanes. Also, at some appropriate time(s) use the formula 1 + tan2 9 = 1 cos2 9

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