The three-dimensional morphology of the flat-shaped spumellarian radiolarian Dictyocoryne was analysed using a microfocus X-ray CT with a special focus on whether it was capable of a planktonic lifestyle. Two types of 3D models, the shell model, which represents a realistic 3D shell, and the wrapped model, which mimics the whole body outline without pseudopodia, were reconstructed in order to estimate volume, surface area, and centres of gravity for the shell model and buoyancy for the wrapped model. The calculated values showed that the volume of shell with respect to the total volume was negatively allometric, regardless of the differences between threshold settings. Stepwise secretions of the patagium layer may result in a comparatively lightweight shell, thereby decreasing the total density during growth but not below the density of seawater. Estimated positions for the centres of gravity and buoyancy were too close to maintain an autonomous posture while floating. Instead, the ratio between surface area and volume was greater than that in an ideal sphere. Such a broad surface area could obtain the viscous resistance necessary for sinking retardation. Spumellarian radiolarians, including Dictyocoryne, have photosynthetic symbionts located primarily in the ectoplasmic layer, which is a habitable space that can be maximised within the larger surface area. Given that radiolarians float when extending their pseudopodia, it can be hypothesised that pseudopodia may play a role in the adjustment of life posture in a hydraulically unstable shell, which can be integrated into sinking retardation, enhancement of photosynthetic activity and manoeuvrability of life posture within a unique flat-shaped morphogenesis.