Lung cancer is a disease of uncontrolled cell growth in tissues of the lung. Computed tomography (CT) shows promise in detecting lung cancers at earlier, more operable stages, when survival is better. CT scans generate multiple 2-D slice images of the lung and digital image processing software is used to combine these images into a 3-D representation of the lung and, in particular, an identified cancer lesion. Various CT scanners use, often different and usually proprietary, software to develop these 3-D images and generate parameters such as lesion volume. Tracking lesion volume is considered a good diagnostic tool for evaluating the results of patient treatment. The Food and Drug Administration (FDA) is conducting research on developing reference cancer lesions, called phantoms, to test CT scanners and their proprietary software. FDA loaned two semi-spherical phantoms to NIST, called Green and Pink, and asked to have the phantoms measured by a coordinate measuring machine (CMM) and the volumes estimated. This report describes in detail both the experimental and computational methods used to estimate the phantoms' volumes as well as a bootstrap method for estimating the uncertainties of the computed volumes. Three sets of CMM measured data were produced. One set of data involved data density measurements of a known calibrated metal sphere. The other two sets were measurements of the two FDA phantoms at two densities, called the coarse set and the dense set. Two computational approaches were applied to the data. In the first approach spherical models were fit to the calibrated sphere data and to the phantom data. The second approach was to model the data points on the boundaries of the spheres with surface B-splines and then use the Divergence Theorem to estimate the volumes. The results for the coarse data set tended to predict the volumes as expected with low expanded uncertainties and the results did show that the Green phantom was very near spherical. This was confirmed by both computational methods. The spherical model did not fit the Pink phantom as well and the B-spline approach provided a better estimate of the volume in that case. The results for the dense data set did not provide as nice a prediction of volumes as the coarse data set and produced larger expanded uncertainties. A discussion of some possible reasons for these results will be given in the conclusion section. The report includes the MATLAB codes used in the study.