Chapter 5.3, Problem 16P

Prove the following two theorems of Pappus:

Let a curve $y=f\left(x\right)$ be revolved about the x axis, thus forming a surface of revolution. Show that the cross sections of this surface in any plane $x=$ const. [that is, parallel to the $\left(y,z\right)$ plane] are circles of radius $f\left(x\right)$.

Thus write the general equation of a surface of revolution and verify the special case $f\left(x\right)=x^2$ in (3.9).