While analysis of the image noise-power spectrum (NPS) and noise-equivalent quanta (NEQ) are important aspects of imaging system characterization, such metrics are in themselves insufficient descriptions of imaging performance in that they make no account of the imaging task. This paper seeks to quantitatively incorporate imaging task in imaging performance evaluation by combining NEQ with a variety of idealized spatial-frequency-dependent task functions to yield the model observer detectability index. The approach is applied to the case of fully 3D volumetric imaging by flat-panel detector cone-beam CT through analysis of 3D detectability for conditions of varying dose, reconstruction filter, and voxel size. Generalization of the NEQ through incorporation of background "anatomical" noise suggests significant degradation in model observer performance, and the effect is quantified for a variety of detection and discrimination tasks. For anatomical noise modeled according to 1/f b statistics in power-spectral density, the effect is shown to be most severe for low-frequency detection tasks, and somewhat less for mid-to-high spatial frequency tasks, such as discrimination and localization. By considering the fully 3D NEQ, which is known to be asymmetric for cone-beam CT, a compelling hypothesis is realized regarding the detection of structures in volumetric CT images - specifically, that the detectability is different in axial versus sagittal / coronal domains due to asymmetry in the NEQ between these domains, compared to the case in which 3D data are fully interrogated (e.g., by a machine algorithm). This has significant implications for 3-D imaging modalities, including flat-panel cone-beam CT, where the NPS exhibits asymmetric frequency characteristics [viz., high-pass (filtered-ramp) in the transverse domain and low-pass in the longitudinal]. The impact of asymmetric NPS characteristics on detectability was investigated by analysis of the 3D detectability for imaging tasks corresponding to detection and discrimination of fine and low-contrast structures.