Biology · Grades 8–11
Surface-area to volume ratio
For a cube, surface area is 6a² and volume is a³. Their ratio decreases as side length increases.
Rule and assumptions
For a cube, surface area is 6a² and volume is a³. Their ratio decreases as side length increases.
SA/V = 6s²/s³ = 6/s for a cube
Worked examples
A cell is modeled as a cube of side 28 µm. Find surface area divided by volume. This geometry is a simplified model. Round to 3 decimal places if needed. Answer in µm⁻¹.
SA/V = 6s²/s³ = 6/s for a cube 6/28 = 0.214
0.214 µm⁻¹
A cell is modeled as a cube of side 4 µm. Find surface area divided by volume. This geometry is a simplified model. Round to 3 decimal places if needed. Answer in µm⁻¹.
SA/V = 6s²/s³ = 6/s for a cube 6/4 = 1.5
1.5 µm⁻¹
Try two questions
A cell is modeled as a cube of side 25 µm. Find surface area divided by volume. This geometry is a simplified model. Round to 3 decimal places if needed. Answer in µm⁻¹.
A cell is modeled as a cube of side 14 µm. Find surface area divided by volume. This geometry is a simplified model. Round to 3 decimal places if needed. Answer in µm⁻¹.
Answers and reasoning
Answers and marking notes
- 0.24 µm⁻¹
SA/V = 6s²/s³ = 6/s for a cube 6/25 = 0.24
- 0.429 µm⁻¹
SA/V = 6s²/s³ = 6/s for a cube 6/14 = 0.429
Further reading and review references
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