Official comment
That is a pretty hard situation to handle. When making volume measurements we basically create a surface between all of the points around the perimeter and see what is above it. Since the points around the inside of the bins are not on the ground level that you want to make your measurements from the measurement will be way off. It will however provide a good estimate for the areas that are outside of the bin and that are harder to quantify. There really isn't any way to make your measurement using most 3d tools.
The only way I can think of doing it is to select that area in QGIS and then fill it with the base level you want to subtract from it and then sum up all of the pixels inside it. It isn't easy but it is possible.
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