The numerical simulation of three-dimensional hypersonic flows is critical to control the trajectory, the aerodynamic and thermal loads undergone by flight vehicles. Such flows are characterized by intense shock- and rarefaction-waves, as well as high thermal fluxes and are modelled by the Navier-Stokes equations, which can be decomposed into an inviscid part: the Euler equations, plus a viscous and conductive part. Solving the Euler equations over three-dimensional unstructured grids, is often the most demanding part for the numerical methods in terms of robustness and accuracy. Recent work [2] has been conducted to build an original way of solving hyperbolic systems of conservation laws by means of a cell-centered subface based Finite volume method and multidimensional aware simple approximate Riemann solver. This approach is insensitive to the usual Carbuncle phenomenon or odd-even decoupling on two-dimensional unstructured meshes [2]. The first-order explicit time discretization is able to ensure a positive mass density and specific internal energy under a reasonable time step condition. In the present work, we extend this novel approach to 3D geometry and second-order space-time discretization. We assess the ability of this numerical method to solve classical 3D test cases like the spherical Sod problem, the spherical Sedov problem and a Mach 20 blunt-body problem using tetrahedral, prismatic and hexahedral grids. Finally, we make comparisons with in- flight data for the Atmospheric Reentry Demonstrator and the PreX vehicle taken from [1]