Can someone help me out on this problem?

We are supposed to find the volume using integrals. Meaning as x or y changes, the cross-sectional area will change, so we find the equation for the cross sectional area, and then take the integral of it across the height.

In this one, I figured the cross-sectional area =

And if we set the bottom of the blue section along the x-axis, then it would be integrated from 0 to h, so

volume =

volume =

volume =

But somehow I'm supposed to incorporate the radius.

Back of the book says the answer is

edit: well, part of my problem, I think is that I should be puting the cross-sectional area in terms of y. And I think I should be using the equation of a circle: x^2=r^2-y^2. That still doesn't get me the right answer, but it's much closer to theirs, as this would become

so getting closer :/ But this method seems like it would integrate just the top half of the circle. So somehow I need to remove that gap between the circle's center, and the bottom of h.