Drape Shapes to Surface to Get a Solids
Jowenn Lua shows a work around on how to produce 3D Solids with Property Set volumes from a polyline shape draped onto a Civil 3D Surface.
From the Autodesk AKN Civil 3D Screencasts
See Jowenn Lua's AKN page
An interesting quick and dirty method to get to the goal.
You could also employ surface projected Feature Lines and offsets of those to produce the results with the Civil 3D volume tools and reports.
People also tend to forget that Parcel Segments are potential grading features which is another way related to the Feature Line method to attack the problem.