Three silicate glasses were hydrated at high pressure and then heated at atmospheric pressure to exsolve the water into bubbles and create foams. The bubble size distribution in these foams was measured by x-ray microtomography on the GSECARS BM-13 beamline at the Advanced Photon Source. The bubble area distributions were measured in two dimensions using the image slices produced from the microtomography and the software ImageJ. The bubble volume distributions were measured from the three-dimensional tomographic images with the BLOB3D software. We found that careful analysis of the microtomography data in both two and three dimensions was necessary to avoid the physically unrealistic, experimental artifact of identifying and counting many small bubbles whose surfaces were not defined by a septum of glass. When this artifact was avoided the foams demonstrated power-law distributions of bubble sizes in both two and three dimensions. Conversion of the power-law exponents for bubble areas measured in two dimensions to exponents for bubble volumes usually agreed with the measured three dimensional volume exponents. Furthermore, the power-law distributions for bubble volumes typically agree with multiple theories of bubble growth, all of which yield an exponent of 1 for the cumulative bubble volume distribution. The measured bubble volume distributions with exponents near 0.3 can be explained by diffusive growth as proposed by other authors, but distributions with exponents near 1.4 remain to be explained and are the subject of continuing research on the effects of water concentration and melt viscosity on foaming behavior.