I don't believe this is too difficult of a problem but it's been a very long time since I've studied volume of solids and I'm still having a lot of trouble with these questions, if someone could help me set up the integral for this one it would be awesome!

Question: The base of the solid is the region between the x-axis and the parabola . The vertical cross-sections of the solid perpendicular to the y-axis are semicircles. Compute the volume of the solid.

I don't have a lot of work so far:

Since the cross-sections are perpendicular to the y-axis I started out by stating this in terms of x.

and

The graph then crosses the y-axis at y=4...would the limits be from y = 0 to y = 4?

I am also stuck on determining what the radius of the semicircle cross-section would be.