Abstract <p>Eulerian finite-volume schemes intended for gas flow computations in a Cartesian coordinate system are considered. The schemes involve the Gaussian method for discretizing the divergence and gradient operators and the midpoint rule for approximating integrals over cell faces. Sufficient conditions are determined under which such schemes preserve spherical symmetry on a spherical grid. Two approaches are proposed for satisfying a geometric condition concerning the ratio of the areas of corner faces to the cell volume: area correction and a special choice of polar angle partitioning. As an example of symmetry preservation under the sufficient conditions, a spherical Riemann problem is computed by applying a Godunov-type Eulerian scheme.</p>