Question

Hi, I have a calculus question that I just cannot figure out, it is about volume of cross sections.
I would very much appreciate it if someone could figure out the answer and show me all the steps.

A solid has as its base the region bounded by the curves y = -2x^2 +2 and y = -x^2+1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane, upper base equal to 1/2 the length of the lower base, and height equal to 2 times the length of the lower base.

Thanks in Advance :D