Final answer:
When the dimensions of a cubic cell are doubled, the volume increases 8-fold. This example demonstrates the challenge larger cells face with a decreased surface area-to-volume ratio, hindering efficient nutrient and waste exchange.
Step-by-step explanation:
The question concerns how the volume of a cell changes as its dimensions are scaled up. If a cell is a cube and each side is doubled in length from 1 to 2 units, we can calculate the change in volume by cubing the length of any side. For the original cube with sides of 1 unit: Volume = 1 unit x 1 unit x 1 unit = 1 cubic unit. After doubling the sides to 2 units, the new volume is: Volume = 2 units x 2 units x 2 units = 8 cubic units.
Therefore, the volume increases 8-fold from the original size when the dimensions of the cube are doubled. This significant increase in volume compared to the relatively smaller increase in surface area is one of the reasons cells maintain a high surface area-to-volume ratio; it allows for efficient exchange of nutrients and wastes with the environment. Larger cells have more difficulty in this exchange due to the decrease in surface area relative to volume.