As found in Exercise 39, the centroid of the semicircle y = √a² - x² lies at the point (0, 2a/π). Find the area of the surface generated by revolving the semicircle about the line y = x - a.

Data from in Exercise 39

Use Pappus’s Theorem for surface area and the fact that the surface area of a sphere of radius a is 4πa² to find the centroid of the semicircle y = √a² - x².