Question asks:

Find the volume of the solid bounded by: z = 4x^2 + y^2 and the cylinder y^2+z=2

In the solution they used change of variable by putting in x = r cosθ/sqrt 2 and

y = r sin θ, z = z

this looks like cylindrical co ordinates to me, but I thought that you always use

x = r cos θ

can someone explain why divide it by root 2? And how can you just look at questions like these and decide what change of variable to make? I'm really confused.