Small angle neutron scattering (SANS) is used to measure the absolute density of water contained in 1-D cylindrical pores of a silica material MCM-41-S with pore diameters of 19 and 15 angstrom. By being able to suppress the homogeneous nucleation process inside the narrow pore, one can keep water in the liquid state down to at least 160 K. From a combined analysis of SANS data from both H2O and D2O hydrated samples, we determined the absolute value of the density of I-D confined water. We found that the average density of water inside the fully hydrated 19 A pore is 8% higher than that of the bulk water at room temperature. The temperature derivative of the density shows a pronounced peak at T-L = 235 K signaling the crossing of the Widom line at ambient pressure and confirming the existence of a liquid-liquid phase transition at an elevated pressure. Pore size and hydration level dependences of the density are also studied.