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One of the examples in the Wikipedia article for parametric surfaces gives the formula for parametrizing a surface of revolution. Following that example, here are the plots I produced with sage's parametric_plot3d function-- are these what you were hoping for?

sage: var('u,phi')
(u, phi)
sage: parametric_plot3d([u*cos(phi), u*sin(phi), sin(u)], (u, 0, 2*pi), (phi, 0, 2*pi), aspect_ratio=1)

sage: parametric_plot3d([u*cos(phi), u*sin(phi), sqrt(1 - (u-2)^2)], (u, 0, 3), (phi, 0, 2*pi), aspect_ratio=1)