Subwavelength diameter semiconductor nanowires can support optical resonances with anomalously large absorption cross sections, and thus tailoring these resonances to specific frequencies could enable a number of nanophotonic applications. Here, we report the design and synthesis of core/shell p-type/intrinsic/n-type (p/i/n) Si nanowires (NWs) with different sizes and cross-sectional morphologies as well as measurement and simulation of photocurrent spectra from single-NW devices fabricated from these NW building blocks. Approximately hexagonal cross-section p/i/n coaxial NWs of various diameters (170-380 nm) were controllably synthesized by changing the Au catalyst diameter, which determines core diameter, as well as shell deposition time, which determines shell thickness. Measured polarization-resolved photocurrent spectra exhibit well-defined diameter-dependent peaks. The corresponding external quantum efficiency (EQE) spectra calculated from these data show good quantitative agreement with finite-difference time-domain (FDTD) simulations and allow assignment of the observed peaks to Fabry-Perot, whispering-gallery, and complex high-order resonant absorption modes. This comparison revealed a systematic red-shift of equivalent modes as a function of increasing NW diameter and a progressive increase in the number of resonances. In addition, tuning shell synthetic conditions to enable enhanced growth on select facets yielded NWs with approximately rectangular cross sections; analysis of transmission electron microscopy and scanning electron microscopy images demonstrate that growth of the n-type shell at 860 °C in the presence of phosphine leads to enhanced relative Si growth rates on the four {113} facets. Notably, polarization-resolved photocurrent spectra demonstrate that at longer wavelengths the rectangular cross-section NWs have narrow and significantly larger amplitude peaks with respect to similar size hexagonal NWs. A rectangular NW with a diameter of 260 nm yields a dominant mode centered at 570 nm with near-unity EQE in the transverse-electric polarized spectrum. Quantitative comparisons with FDTD simulations demonstrate that these new peaks arise from cavity modes with high symmetry that conform to the cross-sectional morphology of the rectangular NW, resulting in low optical loss of the mode. The ability to modulate absorption with changes in nanoscale morphology by controlled synthesis represents a promising route for developing new photovoltaic and optoelectronic devices.