This work presents a beamforming procedure that significantly reduces the number of operations when performing volumetric synthetic aperture imaging with row-column addressed arrays (RCAs). The proposed beamformer uses that the image values along the elevation direction of the low-resolution volume (LRV) are approximately constant. It is thus hypothesized that the entire LRV could be reconstructed from a single 2-D cross section of the LRV. The presented method contains two stages. The first stage beamforms, for each emission, a cross section using the conventional RCA beamformer. The second stage extrapolates the rest of the image points in the volume from the 2-D cross sections. Assuming the image volume is covered by 3-D grid coordinates with a size of Nw×Nw ×Nz , i.e., Nw samples along the x - and y -axis and Nz samples along the z -axis, the proposed beamformer reduces the number of mathematical operations by a factor of approximately NNw/(NS+Nw) . Here, S is the ratio between the first- and second-stage axial sampling rates, and N is the receiving aperture's number of channels. Beamforming a 128×128×1024 volume from data acquired with N = 128 receiving channel can thus be achieved with 25.6 times fewer operations, when S = 4. A 9.23 times increase in the beamforming rate for a 100×100×200 volume was demonstrated on complex data from a 128 + 128 Vermon RCA probe. Real-time volumetric beamformation can, with this increase, be performed with a pulse repetition frequency of up to 1804.80 Hz. The proposed and conventional beamformer's output was visually indistinguishable, and the full width at half maximum (FWHM) and full width at tenth maximum (FWTM) were at most 1.19% larger with the proposed approach. The proposed beamformer can thus perform volumetric imaging significantly faster than the current approach, with a negligible difference in image quality.