Density is a material property, independent of shape or size

Steps:

• Density ρ = mass/volume; for same material, ρ is identical regardless of dimensions.
• Both cylinders are copper, so they share the same intrinsic density.
• Height of P (h_P = 2h_Q) and diameter of P (d_P = 0.5 d_Q) affect volume, but mass scales proportionally.
• Thus, ρ_P = ρ_Q, as volume and mass ratios cancel out.

Why C is correct:

• Density is defined as a characteristic of the material (copper), not its geometry, so both have equal density.

Why the others are wrong:

• A: Density does not scale with volume ratios; it's material-specific.
• B: No factor of two relates to density; dimensions affect size, not material property.
• D: Halving diameter does not halve density; both are pure copper.

Final answer: C