Surface Area to Volume Ratio for a Cylinder

Steps:

• Radius r = diameter / 2 = 0.5 μm / 2 = 0.25 μm.
• Volume V = π r² h = π (0.25)² (2.0) = π (0.0625)(2) = 0.125 π μm³.
• Total surface area SA = 2 π r h + 2 π r² = 2 π (0.25)(2) + 2 π (0.0625) = π + 0.125 π = 1.125 π μm².
• Ratio SA / V = 1.125 π / 0.125 π = 9, or 9:1.

Why D is correct:

• For a cylinder, SA / V = (2 π r h + 2 π r²) / (π r² h) simplifies to 9 with given dimensions.

Why the others are wrong:

• A: 3.0:1 – underestimates by treating as a sphere or ignoring ends.
• B: 5.0:1 – mismatches cylinder formula, possibly confusing with different shape.
• C: 8.0:1 – uses only lateral surface area, excluding end caps.

Final answer: D