Diffusion rate depends on surface area to volume ratio

Steps:

• Acid diffuses into agar from the surface, decolorizing the indicator.
• Smaller blocks have higher surface area relative to volume, allowing faster diffusion.
• Calculate SA/V for each: A (3×3×3) = 6.00 mm⁻¹; B (6×6×6) = 3.00 mm⁻¹; C (6×12×12) = 1.75 mm⁻¹; D (12×12×12) = 1.50 mm⁻¹.
• Highest SA/V means quickest color change.

Why A is correct:

• A has the highest SA/V ratio (6.00 mm⁻¹), maximizing acid penetration speed per Fick's law of diffusion.

Why the others are wrong:

• B: Lower SA/V (3.00 mm⁻¹) than A, so slower diffusion.
• C: Even lower SA/V (1.75 mm⁻¹) due to elongated shape, reducing relative surface exposure.
• D: Lowest SA/V (1.50 mm⁻¹), minimizing diffusion rate.

Final answer: A