Resistance scales with length over area, volume conserved

Steps:

• Resistance formula: R = ρ L / A (ρ: resistivity, L: length, A: cross-sectional area).
• Volume V = A L remains constant.
• New length L' = 2L, so new area A' = V / L' = (A L) / (2L) = A / 2.
• New resistance R' = ρ (2L) / (A/2) = 4 (ρ L / A) = 4R.

Why D is correct:

• Per Ohm's law, R ∝ L/A; doubling L and halving A (to conserve volume) multiplies R by 4.

Why the others are wrong:

• A: Assumes R halves, as if L halved and A doubled, opposite of changes here.
• B: Assumes no change, ignoring dimensional shifts from rolling.
• C: Assumes only L doubles with A unchanged, violating constant volume.

Final answer: D