NOTE The top two graphs are wrong Find parametric equations

NOTE: The top two graphs are wrong.

Find parametric equations for the surface obtained by rotating the curve x = 81^2 - y^4, -9 = y = 9, about the y-axis. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of theta and/or v.) x = (81y^2 - y^4) cos(theta), y = y, z = (81y^2 - y^4) sin (theta) (where -9 = y = 9) Use the parametric equations found above to graph the surface.

Solution

here two graphs of top are wrong, so here remains two.

and one of them ( option D ) is wrong because that is not equally distributed. So here is answer is C.