Calculating Surface Area to Volume Ratio

Laura Armstrong & Joe Wolfensohn

Teachers

Surface Area to Volume Ratio (SA:V)

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How SA:V Affects Body Size and Metabolism

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Laura Armstrong

Head of Biology

Joe Wolfensohn

Assistant Head of Biology

Recall Questions

This topic requires prior knowledge of mathematical concepts including surface area and volume, and understanding of diffusion.

Define diffusion.

Net movement of particles from an area of higher concentration to an area of lower concentration

Explain how increasing temperature affects the rate of diffusion.

As temperature increases the kinetic energy of particles increases. The particles are moving faster so the rate of diffusion is greater

State 3 other factors that increase the rate of diffusion.

Concentration gradient, surface area, thickness of exchange surface

Topic Explainer Video

Check out this @JoeDoesBiology video that explains calculating surface area to volume ratio, then read the study notes. Once you’ve gone through them, don’t forget to try the practice questions!

Surface Area to Volume Ratio (SA:V)

Cubes:

Surface area (SA) = 6 × (side length)²
Volume (V) = (side length)³
SA:V ratio = SA ÷ V

Example:
For a cube with a side length of 1 cm:

SA = 6 × (1²) = 6 cm²
V = 1³ = 1 cm³
SA:V = 6 ÷ 1 = 6:1

For a cube with a side length of 2 cm:

Diagram of a 1 cm × 1 cm × 1 cm cube used to illustrate how surface area and volume relate for diffusion and transport in cells.

SA = 6 × (2²) = 24 cm²
V = 2³ = 8 cm³
SA:V = 24 ÷ 8 = 3:1

For a cube with a side length of 3 cm:

Diagram of a 2 cm × 2 cm × 2 cm cube divided into smaller cubes to illustrate how increasing size reduces surface area to volume ratio for diffusion.

SA = 6 × (3²) = 54 cm²
V = 3³ = 27 cm³
SA:V = 54 ÷ 27 = 2:1

As the size of an object or organism increases its surface area:volume decreases.

Cuboids:

SA = 2(lw + lh + wh)
V = l × w × h
SA:V ratio = SA ÷ V

Example:
For a cuboid with dimensions 4 cm × 2 cm × 4 cm:

$Diagram of a 4 cm × 4 cm × 2 cm rectangular block divided into smaller cubes to illustrate how changing dimensions affects surface area to volume ratio for diffusion.$

SA = 2(4×4 + 4×2 + 4×2) = 64 cm²
V = 4 × 2 × 4 = 32 cm³
SA:V = 64 ÷ 32 = 2:1

If the object is flattened the SA:V increases.

Cylinders:

SA = 2πr² + 2πrh
V = πr²h
SA:V ratio = SA ÷ V

Example:
For a cylinder with r = 2 cm and h = 5 cm:

$Diagram of a cylinder with radius 2 cm and height 5 cm used to calculate surface area and volume for diffusion-related surface area to volume ratio questions.$

SA = 2π(2²) + 2π(2)(5) = 8π + 20π = 28π ≈ 87.96 cm²
V = π(2²)(5) = 20π ≈ 62.83 cm³
SA:V ≈ 1.4:1

How SA:V Affects Body Size and Metabolism

Increasing SA for Exchange

Flattened shape (e.g., leaves, flatworms) → More surface area for gas exchange by diffusion.
Folding of surfaces (e.g., villi in intestines, alveoli in lungs) → More efficient absorption.
Projections (e.g., root hair cells, microvilli) → Increased nutrient uptake.

Decreasing SA to Conserve Heat

Compact shape (e.g., Arctic fox, round body structure) → Reduces heat loss.
Fat insulation (e.g., blubber in whales) → Reduces heat loss.
Reduced extremities (e.g., smaller ears in polar bears) → Less surface area exposed to cold and therefore less heat loss.