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S is a region on the plane 7x + 8y + 3z  =  4 contained within...

S is a region on the plane 7x + 8y + 3z  =  4 contained within the vertical cylinder px2 + qy2  =  R2. The base of the cylinder, A, where it interescts the xy-plane, is an ellipse.

If the area of A, the portion of the xy-plane within the cylinder, is 14.7, what is the surface area of S?

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