Attached is a plot of the base with one of the cross sections (at

).
The area of any one cross section is given by

, where

is the radius of the circular cross section. In terms of the sections' diameters

, the area would be

.
Each section's diameter is determined by the vertical distance (in the x-y plane) between the curve

and the x-axis (

), or simply

. So the area of any one cross-section for a given

is

.
The region extends from

to

(the positive root of

), so the volume of the solid would be

You can compute this by expanding the integrand, then integrating term by term. You should find a volume of

.