To demonstrate the feasibility of 3D echo-planar spectroscopic imaging (EPSI) technique with rapid volumetric radial k-space sampling for hyperpolarized (HP) 13C magnetic resonance spectroscopic imaging (MRSI) in vivo. A radial EPSI (rEPSI) was implemented on a 3 T clinical PET/MR system. To enable volumetric coverage, the sinusoidal shaped readout gradients per k-t-spoke were rotated along the three spatial dimensions in a golden-angle like manner. A distance-weighted, density-compensated gridding reconstruction was used, also in cases with undersampling of spokes in k-space. Measurements without and with HP 13C-labeled substances were performed in phantoms and rats using a double-resonant 13C/1H volume resonator with 72 mm inner diameter. Phantom measurements demonstrated the feasibility of the implemented rEPSI sequence, as well as the robustness to undersampling in k-space up to a factor of 5 without advanced reconstruction techniques. Applied to measurements with HP [1-13C]pyruvate in a tumor-bearing rat, we obtained well-resolved MRSI datasets with a large matrix size of 123 voxels covering the whole imaging FOV of (180 mm)3 within 6.3 s, enabling to observe metabolism in dynamic acquisitions. After further optimization, the proposed rEPSI method may be useful in applications of HP 13C-tracers where unknown or varying metabolite resonances are expected, and the acquisition of dynamic, volumetric MRSI datasets with an adequate temporal resolution is a challenge.