Surface Area vs. Volume Scaling in Cubes

Steps:

• Surface area of cube: SA = 6s²; volume: V = s³, where s is side length.
• Plotting SA and V against s shows V increasing faster (cubic vs. quadratic), so volume line steeper.
• Line 1 (steeper) represents volume; line 2 (less steep) represents surface area.
• SA:V ratio = 6s²/s³ = 6/s, which decreases as s increases.

Why C is correct:

• Matches formulas: steeper line 1 is volume (s³), shallower line 2 is surface area (s²), and ratio 6/s decreases with larger s.

Why the others are wrong:

• A: Swaps lines; line 1 is volume, not surface area.
• B: Swaps lines and effect; ratio decreases, does not increase.
• D: Swaps effect; ratio decreases, does not increase.

Final answer: C