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There is a useful plugin for Sketchup called VolumeCalculator21.rb. It allows us to calculate the volume of an object. The only requirements are that it needs the object to be a group or component, and for maximum accuracy the geometry has to be clean. For clean geometry basically we need that each edge has two faces, no more no less, but that will ensure that the volume calculation is precise.
I tried it with basic geometry and the results were exact, when I tried it with very complex and not clean geometry, I got different results from time to time, so the importance of using clean geometry is very clear.
Still, I think it is a plugin worth having. To use it (after downloading the plugin and saving it to the plugins folder in SketchUp) select the group or component you want to know its volume, right click, and you will find an option called volume. Select that and you will get a dialog box that will ask you for which units you want to use and other options. It is very simple to use.
You can download the plugin here. Thanks to the author TGI.