Prominence cavities in coronal helmet streamers are readily detectable in white-light coronagraph images, yet their interpretation may be complicated by projection effects. In order to determine a cavity's density structure, it is essential to quantify the contribution of noncavity features along the line of sight. We model the coronal cavity as an axisymmetric torus that encircles the Sun at constant latitude and fit it to observations of a white-light cavity observed by the Mauna Loa Solar Observatory (MLSO) MK4 coronagraph from 2006 January 25 to 30. We demonstrate that spurious noncavity contributions (including departures from axisymmetry) are minimal enough to be incorporated in a density analysis as conservatively estimated uncertainties in the data. We calculate a radial density profile for cavity material and for the surrounding helmet streamer (which we refer to as the "cavity rim") and find that the cavity density is depleted by a maximum of 40% compared to the surrounding helmet streamer at low altitudes (1.18 R☉) but is consistently higher (double or more) than in coronal holes. We also find that the relative density depletion between cavity and surrounding helmet decreases as a function of height. We show that both increased temperature in the cavity relative to the surrounding helmet streamer and a magnetic flux rope configuration might lead to such a flattened density profile. Finally, our model provides general observational guidelines that can be used to determine when a cavity is sufficiently unobstructed to be a good candidate for plasma diagnostics
