It was found that filaments observed in EUV could be much more extended than in H$\alpha$. These extended dark structures visible in EUV are named EUV filaments. Their parts seen only in EUV (not observable in H$\alpha$ because of low opacity at the H$\alpha$ wavelength) are called EUV-filament extensions (or simply EUV extensions). For the EUV filament observed by SoHO on 15 October 1999 as northern polar crown filament, only a few small dark structures were seen in H$\alpha$. This suggests that the mass of the EUV extension is larger than, or at least comparable with, the mass of the parts of the filament observed in H$\alpha$. In our previous work we determined the 3D structure of the EUV extension of this EUV filament. In this paper we present the determinations of mass and average density of this EUV extension. For better density estimates we interpret the hydrogen Lyman lines observed by SUMER using non-LTE radiative transfer code. From the best fitting of Lyman lines we obtained a reasonable model of the EUV extension with low gas pressure, temperatures from 2$\times10^4$ K to $10^5$ K and with extended prominence-corona transition regions.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html