Chapter 6.7, Problem 39ES

Use the Theorem of Pappus and the fact that the volume of a sphere of radius $a$ is $V=\frac{4}{3}\pi a^3$ to show that the centroid of the lamina that is bounded by the $x\text{-axis}$ and the semicircle $y=\sqrt{a^2-x^2}$ is $\left(0,4a/\left(3\pi \right)\right)$ . (This problem was solved directly in Example $3$ .)