Surface Area to Volume Ratio and Diffusion

Steps:

• Smaller agar cubes have higher surface area to volume (SA:V) ratios, allowing faster acid diffusion.
• 1 cm cube: SA:V = 6:1; acid penetrates fully (0.5 cm to center) in 10 min, changing color completely.
• 3 cm cube: SA:V = 2:1; acid penetrates slower, reaching only 0.5 cm depth from surface.
• Results show complete change for 1 cm and partial (0.5 cm) for 3 cm, matching option A.

Why A is correct:

• High SA:V in small cubes enables complete diffusion; low SA:V in large cubes limits penetration depth proportionally to half the side length (0.5 cm for 3 cm cube).

Why the others are wrong:

• B: 1 cm depth for 3 cm cube overestimates diffusion, ignoring reduced SA:V.
• C: 0.25 cm for 1 cm underestimates; small size allows full penetration.
• D: 0.5 cm for 1 cm underestimates full change; 1 cm for 3 cm overestimates limited diffusion.

Final answer: A