Can xBim toolkit help me calculate the volume of some objects in an IFC model?

I am new to .NET xBim Toolkit and I wonder if it can help with calculating the volume of some objects in an IFC model. In particular, there is module called XbimGeometry but I am unsure if and how it could be used for this purpose. Or if it is just meant for graphics.

Yes it can. In Xbim.Geometry v5.1 (the latest in develop/master) you can calculate the volume of some IFC geometry primitives.

Typically the Geometry Engine is used to create a Scene which is tessellated / meshed, but it can also be used to calculate more fundamental geometry data.

E.g. in this unit test you can see how to get the volume of a single IfcSweptDiskSolid object https://github.com/xBimTeam/XbimGeometry/blob/c1c22812601d0bd506c5f9230b731d0ab0c6e08a/Xbim.Geometry.Engine.Interop.Tests/IfcExtrudedAreaSolidTests.cs#L74

            using (var model = MemoryModel.OpenRead("YourModel.ifc"))
            {
                var sweptDisk = model.Instances.OfType<IIfcSweptDiskSolid>().FirstOrDefault();

                // Convert to a solid
                var solid = geomEngine.CreateSolid(sweptDisk, logger);
                solid.Volume.Should().BeApproximately(1234.56, 1e-7);
            }

Clearly this is quite low level, and you'll need to account for voids (holes etc - using the Boolean cut capabilities in the engine), and account the many different geometry types (Sweeps, Breps, Extrusions etc). And remember this code above is a single geometric item that forms part of an Object and could be just one part of a entity's set of shapes. i.e. Objects are often represented by a composite of these individual representations.

i.e. this Window is made up of 4 separate representations:

Whole window Sill Outer Frame Inner Frame Glass Pane

This is just one object and items are much more complex.

So 'calculating the volume' may need a bit of clarifications.

Ultimately your actual answer will depend on what you want to do with the volume data. Do you want to do a material-based quantity take off? Do you just want the overall volume of an object (bear in mind that something like a Wall could have multiple materials and voids)? Do you want a bounding box volume?

There's quite a few improvements in the v6 Xbim.Geometry in this area so may be worth checking that netcore branch out. I believe there are some higher order implementations in that version.