Chapter 14.8, Problem 59ES

These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that lies in the plane of R such that R is entirely on one side of L, then the volume of the solid formed by revolving R about L is given by

$\text{volume}=\left(\text{area of }R\right)\cdot \left(\begin{array}{l}\text{distance}\text{traveled}\\ \text{by}\text{the}\text{centroid}\end{array}\right)$

Use the Theorem of Pappus to find the centroid of the triangular region with vertices $\left(0,0\right),\left(a,0\right),\text{and}\left(0,b\right),$ where $a>0\text{ and }b>0.$