The surface-to-volume ratio of a cell

Options

A. Remains constant
B. Decreases with increasing size
C. Increases with increasing size
D. Both (2) and (3)

Answer

**Step-by-Step Solution:**

1. **Understanding Surface Area and Volume**:
- The surface area (SA) of a cell is the total area that the surface of the cell occupies, while the volume (V) is the amount of space the cell occupies.
- The formulas for these are:
- Surface Area (SA) = \(6a^2\) for a cube (where \(a\) is the length of a side)
- Volume (V) = \(a^3\) for a cube.

2. **Effect of Increasing Cell Size**:
- As the size of the cell increases (i.e., as \(a\) increases), the volume increases at a faster rate than the surface area because volume increases with the cube of the side length, while surface area increases with the square of the side length.
- This means that if you double the length of a side, the volume increases by a factor of \(2^3 = 8\), while the surface area increases by a factor of \(2^2 = 4\).

3. **Calculating Surface-to-Volume Ratio**:
- The surface-to-volume ratio (SA:V) can be expressed as:
\[ \text{SA:V} = \frac{\text{Surface Area}}{\text{Volume}} = \frac{6a^2}{a^3} = \frac{6}{a} \]
- As \(a\) increases, this ratio decreases because the denominator (volume) grows faster than the numerator (surface area).

4. **Conclusion on the Relationship**:
- Therefore, we conclude that as the size of the cell increases, the surface-to-volume ratio decreases.
- Conversely, if the size of the cell decreases, the surface-to-volume ratio increases.

5. **Final Answer**:
- The surface-to-volume ratio of a cell decreases with increasing size.

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