Final answer:
Magnesium is the material that falls under the classification of a class D fire, which pertains to combustible metals requiring specific extinguishing methods.
Step-by-step explanation:
The material that would fall under the classification of a class D fire? is C. Magnesium. Class D fires involve combustible metals, such as magnesium, and require specialized fire extinguishing agents. Materials like cloth and paper (A), lubricating oil (B), electrical wires (D), and gasoline (E) do not fall under the Class D category but are instead classified as Class A, Class B, and Class C fires respectively based on their flammability and the suitable extinguishing methods.