Official comment
There is not a way to do it automatically. You have to draw the measurement polygons for each. You can download the KML file that has all of the volume information by clicking the link that says "KML of Annotations" (shown in the picture under the 'View Full Screen' button.

PS - Please don't post in response to 5 year old threads that are only loosely related to your question. It triggers emails to all users on that thread and I am sure that guy is wondering why he is getting emails.