How to generate a STL from a rotational solid of two equations?
The Wolfram Alpha "Data Download" feature supports STL format, but is only enabled with a Pro Account.

When I click your link to Wolfram, I see the visualization of your equations at the bottom of the page; when I hover over the image, several buttons show below it. One of them is "Data", with a download icon. This gives a number of download options. The File Format drop down includes "STL".