The study of hydration, folding, and interaction of proteins by volumetric measurements has been promoted by recent advances in the development of highly sensitive instrumentations. However, the separation of the measured apparent volumes into contributions from the protein and the hydration water, V(app) = V(int) + Delta V, is still challenging, even with the detailed microscopic structural information from molecular simulations. By the examples of the amyloidogenic polypeptides hIAPP and A beta 42 in aqueous solution, we analyze molecular dynamics simulation runs for different temperatures, using the Voronoi-Delaunay tessellation method. This method allows a parameter free determination of the intrinsic volume V(int) of complex solute molecules without any additional assumptions. For comparison, we also use fused sphere calculations, which deliver van der 'Wags and solute accessible surface volumes as special cases. The apparent volume V(app) of the solute molecules is calculated by different approaches, using either a traditional distance based selection of hydration water or the construction of sequential Voronoi shells. We find an astonishing coincidence with the predictions of a simple empirical approach, which is based on experimentally determined amino acid side chain contributions (Biophys. Chem. 1999, 82, 35). The intrinsic volumes of the polypeptides are larger than their apparent volumes and also increase with temperature. This is due to a negative contribution of the hydration water Delta V to the apparent volume. The absolute value of this contribution is less than 10% of the intrinsic volume for both molecules and decreases with temperature. Essential volumetric differences between hydration water and bulk water are observed in the nearest neighborhood of the solute only, practically in the first two Delaunay sublayers of the first Voronoi shell. This also helps to understand the pressure dependence of the partial molar volumes of proteins.