The correct answer is A) relieved stresses. Radial cracks in the castable refractory of the burner cones after the first firing indicate that the refractory material has experienced thermal stresses during the heating process, which have been relieved through the formation of these cracks. This is a common occurrence when new refractory materials are installed, as they need to adjust to the thermal conditions of the furnace. The other options are incorrect because: B) Patchwork may be a solution, but the cracks themselves indicate a more fundamental issue with the refractory material. C) The cone angle is not the primary cause of the cracking. D) Plastic firebrick is a different type of refractory material, not applicable to this situation.