The correct answer is option 3: the two wires must be of different materials.

Resistivity is the intrinsic property of a material that determines its resistance to the flow of electric current. Different materials have different resistivities, so two wires made of different materials will have different resistances, even if they have the same length and volume.

Option 1 is incorrect because having different cross-sections does not necessarily mean that the wires will have different resistances. The resistance of a wire depends on its resistivity and length, not its cross-section area.

Option 2 is also incorrect because having different temperatures may affect the resistance of a wire, but it will not be the sole reason for the two wires to have different resistances. The temperature coefficient of resistance is a property of the material, so it would still depend on the materials used.

Option 4 is irrelevant to the resistance of the wires. The density of a material does not have a direct impact on its resistance.

In conclusion, the most significant factor that would cause two wires with equal lengths and equal volumes to have different resistances is that they are made of different materials with different resistivities.