Final answer:
The surface area to volume ratio is important in maintaining homeostasis and the survival of the cell because it determines the rate of exchange of materials between the cell and its environment. As cells increase in size, their surface area to volume ratio decreases, which can hinder nutrient exchange and waste removal. Cells maintain a high surface area to volume ratio through division or the development of specialized structures.
Step-by-step explanation:
The surface area to volume ratio is important in maintaining homeostasis and the survival of the cell because it determines the rate of exchange of materials between the cell and its environment. As a cell increases in size, its volume increases more rapidly than its surface area. This means that a larger cell will have a lower surface area to volume ratio compared to a smaller cell.
For example, imagine two cells, one with a volume of 1 mm³ and a surface area of 6 mm² (surface area to volume ratio of 6 to 1), and another with a volume of 8 mm³ and a surface area of 24 mm² (surface area to volume ratio of 3 to 1). The larger cell has a lower surface area to volume ratio, which means it will have a harder time exchanging nutrients, gases, and wastes with its environment.
By maintaining a high surface area to volume ratio, cells are able to efficiently carry out essential processes such as obtaining nutrients, expelling waste products, and maintaining proper temperature and pH levels. Cells achieve this by either dividing to stay small or developing specialized organelles that increase their surface area, such as microvilli in intestinal cells.