Radio lobes of a sample of eleven very powerful classical double radio galaxies were studied. Each source was rotated so that the symmetry axis of the source was horizontal, and vertical cross-sectional cuts were taken across the source at intervals of one beam size. These were used to study the cross-sectional surface brightness profiles, the width of each slice, radio emissivity as a function of position across each slice, the first and second moments, and the average surface brightness, minimum energy magnetic field strength, and pressure of each slice. A Gaussian provides a good description of the surface brightness profile of cross-sectional slices. The Gaussian FWHM as a function of distance from the hot spot first increases and then decreases with distance from the hot spot. The width as a function of distance from the hot spot is highly symmetric on each side of the source. The radio emissivity is often close to flat across a slice, indicating a roughly constant emissivity and pressure for that slice. Some slices show variations in radio emissivity that indicate an ``edge-peaked'' pressure profile for that slice; these often occur in slices near the local maxima of the bridge width. The emissivity does not exhibit any signature of emission from a jet. The first moment is generally quite close to zero indicating only small excursions of the ridge line from the symmetry axis of the source. The second moment indicates the same source shape as is found using the Gaussian FWHM. The average magnetic field strength and pressure decrease with increasing distance from the hot spot, reaching a roughly constant value at a location that is typically just before the location of a local maximum of the bridge width. These results are interpreted in terms of a heuristic model for the radio lobes.