The surface area-to-volume ratio of a small cell is larger than that of a large cell. This ratio is important because it affects the cell's ability to transport materials in and out of the cell.
To understand this, consider how surface area and volume change with size:
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Surface Area Calculation: The surface area (SA) of a cell can be approximated by the formula for the surface area of a sphere, which is \(4\pi r^2\), where \(r\) is the radius of the cell.
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Volume Calculation: The volume (V) of a cell can be approximated by the formula for the volume of a sphere, which is \(\frac{4}{3}\pi r^3\).
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Surface Area-to-Volume Ratio: To find the surface area-to-volume ratio (SA:V), you can divide the surface area by the volume: \[ \text{SA:V} = \frac{4\pi r^2}{\frac{4}{3}\pi r^3} = \frac{3}{r} \]
From this equation, you can see that as the radius (or size) of the cell increases, the ratio \(\frac{3}{r}\) decreases. This means that smaller cells have a higher surface area relative to their volume compared to larger cells.
In summary, small cells have a greater surface area-to-volume ratio than larger cells, which enhances their efficiency in nutrient uptake and waste disposal. This relationship is one reason why cells tend to remain small in size.
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