In radar activity recognition, 2D signal representations such as spectrogram, cepstrum and cadence velocity diagram are often utilized, while range information is often neglected. In this work, we propose to utilize the 3D time-range-Doppler (TRD) representation, and design a 3D Orthogonally-Projected EfficientNet (3D-OPEN) to effectively capture the discriminant information embedded in the 3D TRD cubes for accurate classification. The proposed model aggregates the discriminant information from three orthogonal planes projected from the 3D feature space. It alleviates the difficulty of 3D CNNs in exploiting sparse semantic abstractions directly from the high-dimensional 3D representation. The proposed method is evaluated on the Millimeter-Wave Radar Walking Dataset. It significantly and consistently outperforms the state-of-the-art methods for radar activity recognition.