Is there any method that to convert a surface obtained by revolving a function around the x or y axis into a parametric equation?
For example: The function $y = x^3$ for $-3 < x < 3$ when revolved around the y axis forms a bowl like shape. Is there any way to express this surface, or any similar surface as a set of parametric equations?
Any surface of revolution can be easily parametrized. If you start with the parametric curve $(x(u),y(u))$, $u\in I$ (some interval), and rotate it about the $x$-axis, the surface you obtain will be parametrized by $$g(u,v) = \big(x(u), y(u)\cos v, y(u)\sin v\big), \qquad u\in I, \quad v\in [0,2\pi).$$