Chapter 14.4, Problem 58ES

(a) Find parametric equations for the surface of revolution that is generated by revolving the curve $z=f\left(x\right)$ in the $xz\text{-plane}$ about the $z\text{-axis}.$

(b) Use the result obtained in part (a) to find parametric equations for the surface of revolution that is generated by revolving the curve $z=1/x^2$ in the $xz\text{-plane}$ about the $z\text{-axis}\text{.}$

(c) Use a graphing utility to check your work by graphing the parametric surface.