My problem appears in solving volume of body, defined by this equation
(x^2+y^2+z^2) = 4a(x^2+y^2)
I think, that you mean this equation .
We consider the case and multiply by 2 the integral (since this body is symmetrical about the plane ).
Find the body's proection on the plane :
So, (As you can see, this projection is a circle whose radius is equal to ).
We write a set , which limits the surface :
Convert to the cylindrical coordinates .
So, finally you have