Solving Surface Equation Homework

[athrun200]

Homework Statement

Homework Equations

The Attempt at a Solution

It seems very obvious that after rotation, it becomes a circle, so how to write it out mathematically?

That I don't know the general equation of a surface.
Is $y^2+x^2=f^2(x)$ the answer?

 

[Jaynte]

Yes, this is the general equation for a circle

$$f(x)²=x²+y²=r²$$

As seen in the figure, f(x)=radius

And from polar coordinates you can get the equation:

$$x=r*cos(\Theta)$$
$$y=r*sin(\Theta)$$
$$x²+y²=r²(cos²(\Theta)+sin²(\Theta))=r²$$