How can I get the full formula to describe a solid of revolution?
Let's say I got the function $f$, and $y = f(x)$, how can I get of formula that give me $z$ to get the function that create a solid of revolution around any axis(the $y$ axis ? the $x$ axis? an arbitrary $x$ or $y$, a $mx+p$ type function... Any straight line in the space ? ) and on a interval $[I,J]$?
Does it exist, and if yes, how, a method to, just by that, get $z$ to describe the function in the space (something like $y= f(x); z= ...$).