Question: In Exercises use the Second Theorem of Pappus, which is stated as follows. If a segment of a plane curve C is revolved about an

In Exercises use the Second Theorem of Pappus, which is stated as follows. If a segment of a plane curve C is revolved about an axis that does not intersect the curve (except possibly at its endpoints), the area S of the resulting surface of revolution is equal to the product of the length of C times the distance d traveled by the centroid of C.

A sphere is formed by revolving the graph of y = √r² - x² about the x-axis. Use the formula for surface area, S = 4πr², to find the centroid of the semicircle y = √² - x².

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