In the Solid Generator dialog, ensure that the solid is enclosed by setting an End Capping Style (right hand side of the dialog). Generally a Flat style is recommended (this will convert the end polygons into solid planes), as this will not interpolate past the feature polygons.
Once an end capping style is set,
Also select to output to a Feature Database -
Then run the Solid Generator.
A Volume (and Surface Area) value will be displayed in the Feature Data pane, and cells can be selected and copied by right clicking, and pasted into another program.