Compared with a smaller cell, a larger cell of the same shape has
a. the same surface-to-volume ratio.
b. a smaller cytoplasm-to-nucleus ratio.
c. less surface area.
d. a smaller average distance between its mitochondria and the nucleus.
e. less surface area per unit of volume.
A, C, and E all seem like they could be the correct answer. Could you please help me?? Thank you!
Yup!
If im understanding your explanation properly, the correct answer is e??
Certainly! Let's analyze the given options to determine the correct answer.
a. The same surface-to-volume ratio: The surface-to-volume ratio is the ratio of the cell's surface area to its volume. When a cell grows larger while maintaining the same shape, its volume increases faster than its surface area. Therefore, the surface-to-volume ratio decreases in a larger cell compared to a smaller one. So, option a is incorrect.
b. A smaller cytoplasm-to-nucleus ratio: The cytoplasm-to-nucleus ratio is the ratio of the cell's cytoplasm (cellular contents excluding the nucleus) to its nucleus. The size of the nucleus does not significantly change as the cell grows larger, whereas the cytoplasm increases in volume. Hence, a larger cell has a smaller cytoplasm-to-nucleus ratio. So, option b is correct.
c. Less surface area: As mentioned earlier, the volume of a larger cell increases more rapidly than its surface area. Therefore, a larger cell will have a relatively smaller surface area compared to a smaller cell. So, option c is correct.
d. A smaller average distance between its mitochondria and the nucleus: The average distance between mitochondria and the nucleus is not determined by the size of the cell. It mainly depends on the organization and arrangement of organelles within the cell. Hence, this option is unrelated to the size of the cell and is incorrect.
e. Less surface area per unit of volume: As discussed, the increase in volume is greater than the increase in surface area as a cell grows larger while maintaining the same shape. Consequently, a larger cell will have less surface area per unit of volume than a smaller cell. Thus, option e is correct.
Therefore, the correct answers are b (a smaller cytoplasm-to-nucleus ratio), c (less surface area), and e (less surface area per unit of volume).
Assume the cell is a sphere. The volume inside a sphere is given by the formula
V = 4/3 pi r^3
where r is the radius of the sphere. This formula was first derived by Archimedes, who showed that the volume of a sphere is two-thirds that of a circumscribed cylinder. (This assertion follows from Cavalieri's principle.) In modern mathematics, this formula is most easily derived using integral calculus, e.g. using disk integration.
The surface area of a sphere is given by the formula
A = 4 pi r^2
This should help you to answer your question. Thanks for asking.