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I want to use Pappus's theorem.S=2*Pi*x*s

The surface S, is 2*Pi*r^2 and the length of the curve s, is Pi*r so the distance from the centroid ,which lies on the y axis by symmetry, to the x axis is S/(2*Pi*Pi*r) = r/Pi

This is not the answer by text book gives for the y coordinate of the centroid. What am I doing wrong? Please help me.