There is at least one Cross Section Volume Report that totals component areas. I am unable to access Ss2 at this time, but I have used it. I believe it is accessed using the End Area Cross Section tool and you must enable certain settings in the dialog box and its leafs that once set, writes an XML file that contains the breakouts and a certain report will list the values. If you can find the XML Report, its help file might explain all of the needed settings.
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