Osteoporosis is a disease caused by decrease in bone density, which makes the bone more susceptible to fractures. The currently used techniques to diagnose osteoporosis such as Dual X-ray Absorptiometry (DXA) and Quantitative Computed Tomography (QCT) are expensive and not widely available. Computerized radiogrammetry is a low cost technique used for the detection of bone loss. But it gives an areal measurement of the cortical bone density. In this paper, we propose a novel low cost technique to measure cortical bone volume for the diagnosis of osteoporosis. The proposed method uses a 3D reconstruction of third metacarpal using three views of hand radiographs and a template model as prior. The projection contours of the template model are registered with the X-ray images and the point-pair correspondence obtained is used to deform the template model. The shaft of the reconstructed bone is used for measuring the cortical volume. The proposed 3D reconstruction method is evaluated by comparison to a ground truth model and manually segmented X-ray images. The cortical volumetric measurements obtained are statistically analyzed for correlation with DXA measurement. The results obtained show that cortical volumetry using the proposed 3D reconstruction method can be developed into a low cost technique for the diagnosis of osteoporosis.