Projection of a 3D scene onto the 2D retina necessarily entails a loss of information, yet perceivers experience a world populated with volumetric objects. Using simultaneous behavioral and neural (fMRI) measures, we identify neural bases of volume perception. Neural activity in the lateral occipital cortex increased with presentation of 3D volumes relative to presentation of 2D shapes. Neural activity also modulated with perceived volume, independent of image information. When behavioral responses indicated that observers saw ambiguous images as 3D volumes, neural response increased; when behavioral data revealed a 2D interpretation, neural response waned. Crucially, the physical stimulus was identical under both interpretations; only the percept of volume can account for the increased neural activity.