Why Are Cells So Small
Introduction
- Topic: Understanding why cells are small.
- Illustration Used: Three cubes of different dimensions (1mm, 2mm, 10mm) are used to explain the concept.
- Key Concept: Surface area to volume ratio.
Surface Area to Volume Ratio
- As cells grow larger, the surface area to volume ratio decreases.
- Smaller cells have a larger surface area to volume ratio.
Mathematical Explanation
Surface Area of a Cube
- Equation: Surface area of a cube = 6 (length x width)
- 1mm Cube: 6 x 1 x 1 = 6 mm²
- 2mm Cube: 6 x 2² = 24 mm²
- 10mm Cube: 6 x 10² = 600 mm²
Volume of a Cube
- Equation: Volume of a cube = length x width x height
- 1mm Cube: 1 x 1 x 1 = 1 mm³
- 2mm Cube: 2 x 2 x 2 = 8 mm³
- 10mm Cube: 10 x 10 x 10 = 1000 mm³
Calculating Surface Area to Volume Ratio
- 1mm Cube: 6/1 = 6:1
- 2mm Cube: 24/8 = 3:1
- 10mm Cube: 600/1000 = 3/5
- Conclusion: Smaller cubes have a larger surface area to volume ratio.
Practical Implications
Ice Example
- Comparison: 1-liter block of ice vs. 1-liter chipped ice.
- Melting Rate: Chipped ice melts faster due to higher surface area to volume ratio.
- Reason: Higher surface area allows faster diffusion of heat.
Application to Cells
- Nutrient and gas diffusion is easier in smaller cells.
- Larger cells face difficulty in diffusing necessary substances.
Conclusion
- Cells are small to maximize the surface area to volume ratio.
- Efficient diffusion of nutrients and gases is crucial for cell function.
End of Lecture: Understanding the need for small cell size through mathematical and practical examples.