Visualizing exactly what is happening with solids of revolution takes a bit of getting used to. Besides going over the relevant sections in the textbook (chapters 6.1, 6.2), you might also find it useful to take a look at some images, videos and other visualization tools available online. Here are some that I recommend:
From www.mathdemos.org:
From Thomas Kiffe’s Calculus Visualizations at Texas A&M:
and finally, here’s a nice interactive visualization tool from Wolfram research:
(you might need to give the applet permission to run - check in your browser’s bar when running for a covert error message/permission query when goint to the webpage!)