You can simply weight your material and compare with the weight of a bulk material with the same dimensions.
If you have it (or access to another lab who has it), you can perform X-ray tomography (it works very well with metal foams, but not every lab is equipped with this kind of instrument...)
If water wets your material there is probably something to do with the water penetration.
If the material is porous, you can measure the void volume by He buoyancy method. (Ideally, with the method by Murata and Kaneko which removes the adsorption effect).
A helium pycnometer is one method you could use, or simply an Avogadro technique of weighing in water and air. Basically you need to estimate the volume by some technique, since getting the mass is easy.