Interest in the use of computed tomography (CT) scanning in animal experimentation has increased markedly over the last decade due to the benefits of studying tissue in live subjects over time. In these experiments, the non-carcass components of the scan are removed from the collected data, allowing scientists to study the carcass of a live animal without the need to slaughter the individual. However, there is not yet a consensus regarding the most appropriate manner in which to convert the CT numbers into a meaningful estimate of area, volume or proportion of tissue present in a carcass at the time of scanning. In this paper we use a Bayesian mixture model to estimate the area of each of three tissue types of interest, fat, muscle and bone present in individual CT scan slices. We then use the Cavalieri principle to estimate the volume and proportion of the carcass attributable to each of these tissues. The approach is validated by analysis of experimental sheep carcasses.