We present 3DeepCT, a deep neural network for computed tomography, which performs 3D reconstruction of scattering volumes from multi-view images. The architecture is dictated by the stationary nature of atmospheric cloud fields. The task of volumetric scattering tomography aims at recovering a volume from its 2D projections. This problem has been approached by diverse inverse methods based on signal processing and physics models. However, such techniques are typically iterative, exhibiting a high computational load and a long convergence time. We show that 3DeepCT outperforms physics-based inverse scattering methods, in accuracy, as well as offering orders of magnitude improvement in computational run-time. We further introduce a hybrid model that combines 3DeepCT and physics-based analysis. The resultant hybrid technique enjoys fast inference time and improved recovery performance.