The correct answer is C) manufacturer's numerical code. The size of ball and roller bearings is typically identified by the manufacturer's numerical code, which provides detailed information about the bearing's dimensions and specifications. This numerical code allows for easy identification and standardization across various bearing types and applications. The other answer choices are incorrect because they do not directly indicate the overall size of the bearing. The inner race cone width (A) and outer ring width (B) are specific dimensions of the bearing, but do not necessarily represent the complete size. The rolling member size (D) is also an important factor, but the manufacturer's numerical code provides a more comprehensive way to identify the bearing size.