The flow about an unyawed cone is considered for the hypersonic moderately low density regime. The shock wave boundary layer interaction is considered in the context of the hypersonic strong interaction approximation. Small transverse curvature and small surface slip effects are considered as perturbations on the basic strong interaction solution. Solutions of the governing two-point boundary value problems are obtained by reduction to a system of ordinary differential equations using double asymptotic expansions in a slip parameter and a hypersonic transverse curvature parameter which is proportional to M2 times the Probstein and Elliott transverse curvature parameter. This implies an additional restriction on the transverse curvature solutions in the hypersonic flow regime. The effect of the self-induced pressure gradient is to increase the skin friction and heat transfer rate at the wall. The first-order slip effect increases the boundary layer mass flow and heat transfer rate. Skin friction surface pressure and displacement thickness are increased for wall-to-stagnation temperature ratios 0.30 and decreased for wall-to-stagnation temperature ratios0.30. The first-order transverse curvature effect decreases the boundary layer mass flow rate, surface pressure, and displacement thickness, whereas the skin friction and wall heat transfer rate are increased.