3D printing has revolutionized the manufacturing of volumetric components and structures in many areas. Several fully volumetric light-based techniques have been recently developed thanks to the advent of photocurable resins, promising to reach unprecedented short print time (down to a few tens of seconds) while keeping a good resolution (around 100 microns). However, these new approaches only work with homogeneous and relatively transparent resins so that the light patterns used for photo-polymerization are not scrambled along with their propagation. Herein, we propose a method that takes into account light scattering in the resin prior to computing projection patterns. Using a tomographic volumetric printer, we experimentally demonstrate that implementation of this correction is critical when printing objects whose size exceeds the penetration depth of light. To show the performances of the scattering corrections we fabricate cell-laden hollow constructs that would be difficult to print otherwise because of light scattering by the cells. Bioprinting cm-scale hollow constructs is therefore challenging but also crucial because hollow channels allow for the inflow of nutrients and oxygen to the cells deep inside the hydrogel. Based on a fine characterization of the scattering process, the proposed scattering correction spatially redistributes light to avoid over-polymerization and clogging the channels, more light is sent to the fine features of the edges while less light is sent to the bulk of the construct. As an example, this technique allowed us to fabricate in 36 seconds a cm-scale construct with four millimetric channels unclogged and a solid core in a soft hydrogel loaded with 4 million HEK 293 cells mL-1. As a comparison, the same printer without the scattering correction yielded clogged channels and a void core. Previous reports have demonstrated the fabrication of similar structures under concentrations of only 10 000 or 1 million cells mL-1 using similar printing technologies. To conclude, this scattering correction extends the capabilities of conventional light-based volumetric printing and opens up promising perspectives in printing inside turbid materials with particular interesting applications for bioprinting cell-laden constructs.