Consider four solids obtained by revolving the regions described in the table about the x-axis over the interval $$[0,1]$$. Assume that the volume for Region 1 is computed as the area between the curves $$y=x$$ (top) and $$y=x^2$$ (bottom), while Regions 2, 3, and 4 are generated by revolving the area under the curves $$y=x^2$$, $$y=x$$, and $$y=\sqrt{x}$$ respectively. Without performing the full integration, determine the relative sizes of these volumes and rank the four regions in increasing order of volume.