A surface of revolution around a coordinate axis should be in one of the following forms:
$y^2 + z^2 = [r(x)]^2$, if revolved about the xaxis
$x^2 + z^2 = [r(y)]^2$, if revolved about the yaxis
$x^2 + y^2 = [r(z)]^2$, if revolved about the zaxis
One must be in one of these forms since a slice of a surface of revolution about an axis creates cross sections that must be circles of varying radii which is noted on the left side of each of these
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