Comparing Volumes of Revolution

Consider four solids generated by revolving the following regions about the x-axis over the interval $$[0, 1]$$:

• Region 1: Bounded by the graphs of $$y=x$$ and $$y=x^2$$.
• Region 2: Bounded by the graph of $$y=x^2$$ and the x-axis.
• Region 3: Bounded by the graph of $$y=x$$ and the x-axis.
• Region 4: Bounded by the graph of $$y=\sqrt{x}$$ and the x-axis.

Without performing integration, arrange the solids corresponding to these regions in order of increasing volume.