Volumetric ultrasound (US) imaging has the potential to provide real-time anatomical imaging with high soft-tissue contrast in a variety of diagnostic and therapeutic guidance applications. However, existing volumetric US machines utilize "wobbling" linear phased array or matrix phased array transducers which are costly to manufacture and necessitate bulky external processing units. To drastically reduce cost, improve portability, and reduce footprint, we propose a rapidly-steered single-element volumetric US imaging system. In this paper we explore the feasibility of this system with a proof-of-concept single-element volumetric US imaging device. The device uses a multi-directional raster-scan technique to generate a series of two-dimensional (2D) slices that were reconstructed into three-dimensional (3D) volumes. At 15 cm depth, 90° lateral field of view (FOV), and 20° elevation FOV, the device produced 20-slice volumes at a rate of 0.8 Hz. Imaging performance was evaluated using an US phantom. Spatial resolution was 2.0 mm, 4.7 mm, and 5.0 mm in the axial, lateral, and elevational directions at 7.5 cm. Relative motion of phantom targets were automatically tracked within US volumes with a mean error of -0.3±0.3 mm, -0.3±0.3 mm, and -0.1±0.5 mm in the axial, lateral, and elevational directions, respectively. The device exhibited a mean spatial distortion error of 0.3±0.9 mm, 0.4±0.7 mm, and -0.3±1.9 in the axial, lateral, and elevational directions. With a production cost near $1000, the performance characteristics of the proposed system make it an ideal candidate for diagnostic and image-guided therapy applications where form factor and low cost are paramount.