Final answer:
Based on cell size alone, the smaller eukaryotic cell would likely have a more active rate of respiration due to a more favorable surface area-to-volume ratio, which facilitates efficient material exchange necessary for respiration.
Step-by-step explanation:
When observing two eukaryotic cells of the same type under the microscope, with one appearing much larger than the other, based on appearance alone, one might expect the smaller cell to be carrying out respiration at a more active rate. This expectation is due to the principle that as a cell increases in size, its surface area-to-volume ratio decreases.
Smaller cells tend to have a higher surface area relative to their volume, which allows for a more efficient exchange of materials such as oxygen and nutrients required for respiration. Mitochondria, the organelles responsible for aerobic cellular respiration, may have difficulty supporting the metabolic needs of a larger cell if the surface area is insufficient to allow the necessary exchange of materials across the cell membrane.
Additionally, eukaryotic cells have evolved structural adaptations to enhance cellular transport, but these adaptations can only compensate up to a point. Although larger eukaryotic cells may contain more mitochondria, the reduced ability of the cell to exchange materials due to a lower surface area-to-volume ratio could lead to a less active rate of respiration, provided all other factors are equal and considering only cell size and not the number and efficiency of the cell's mitochondria.