Final answer:
To calculate the surface area-to-volume ratio of a cell, divide the surface area by the volume. For cube-shaped cells, use 6s² for surface area and s³ for volume. For spherical cells, use 4πr² for surface area and (4/3)πr³ for volume, leading to a ratio of 3/r.
Step-by-step explanation:
To calculate the surface area-to-volume ratio of a cell, you need to compare the cell's outer size to the amount it can hold inside. For instance, if a cell is cube-shaped and has a side length of 's', then its surface area (SA) is 6 times s squared (6s²), and its volume (V) is the cube of side 's' (s³). The ratio is calculated by dividing the surface area by the volume (SA/V).
For a spherical cell, the surface area is given by the formula 4πr², and the volume is given by the formula (4/3)πr³, where r is the radius of the sphere. The surface area-to-volume ratio is, therefore, 3/r. Notably, as a cell grows in size, its surface area increases by the square of its radius, while the volume increases by the cube of the radius, resulting in a decreased surface area-to-volume ratio.
This ratio is essential because it impacts a cell's ability to diffuse substances efficiently. A high surface area-to-volume ratio is preferred for efficient diffusion, which allows cells to absorb nutrients and expel wastes effectively. Cells with low ratios may not allow sufficient exchange, leading to cell division or death to restore an effective ratio.