Surface of Revolution - Equation and Examples

[lgent]

Thank you for this video sir. But I still confused about paraboloid equation (parabola rotated about y/x-axis).
These 3 equations didn't produce the same figure:

(1) x = u
y = v
z = u^2 + v^2

(2) z = x^2 + y^2

(3) x = u.Sin v
y = u.Cos v
z = u^2

Shape (2) and (3) is similar but not exactly the same.
The shape I'm looking for is equation (3).