A systematic computational study of surface reactivity for pure and mono-hydrogenated carbon nanocoes (CNCs) formed from graphene sheets as functions of disclination angle, cone size and hydrogenation sites has been investigated through density functional (DFT) calculations and at the B3LYP/3-21G level of theory. Five disclination angles (60˚, 120˚, 180˚, 240˚ and 300˚) are applied and at any disclination angle four structures with different sizes are studied. For comparison, pure and mono-hydrogenated boron nitride nanocones (BNNCs) with disclination angles 60˚, 120˚, 180˚, 240˚ and 300˚ are also investigated. The hydrogenation is done on three different sites, H S1 (above the first neighbor atom of the apex atoms), H S2 (above one atom of the apex atoms) and H S3 (above one atom far from the apex atoms). Our calculations show that the highest surface reactivity for pure CNCs and BNNCs at disclination angles 60˚, 180˚ and 300˚ is 23.50 Debye for B41N49H10 cone and at disclination angles 120˚ and 240˚ is 15.30 Debye for C94H14 cone. For mono-hydrogenated CNCs, the highest surface reactivity is 22.17 Debye for C90H10-H S3 cone at angle 300˚ and for mono-hydrogenated BNNCs the highest surface reactivity is 28.97 Debye for B41N49H10-H S1 cone when the hydrogen atom is adsorbed on boron atom at cone angle 240˚.