Question

1.3.1 test (cst): cell biology unit test
the table below shows four different cell shapes and sizes, along with their surface - area - to - volume ratios and the distances from the membrane to the center of the cell. for mitochondria located far from the cell membrane, which cell shape and size would be most beneficial for efficient oxygen diffusion, and why?
cell shape surface area - to - volume ratio (μm) distance to center of cell (μm)
0.6 5
0.06 50
0.5 7.5
0.05 75
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a. smaller sphere, because it allows the most rapid movement of nutrients from cell membrane to cell center
b. small cube, because its dimensions allow the most nutrients to enter and move the shortest distance
c. large cube, because its small surface - area - to - volume ratio is most favorable for entry of nutrients
d. rectangular prism, because its shape is most favorable for

Explanation:

• Surface - area - to - volume ratio: A higher surface - area - to - volume ratio (\(0.5\) for the smaller sphere compared to \(0.05\) for the larger sphere and \(0.06\) for the larger cube) means more surface area relative to volume. This is beneficial for diffusion as there is more membrane available for oxygen (a nutrient in this context) to enter the cell.
• Distance to center: The smaller sphere has a shorter distance (\(7.5\ \mu m\)) from the membrane to the center compared to the larger cube (\(50\ \mu m\)) and larger sphere (\(75\ \mu m\)). Shorter distances mean faster diffusion (since diffusion rate is inversely related to the distance over which diffusion has to occur, according to Fick's laws of diffusion, \(J=-D\frac{dC}{dx}\), where \(J\) is the diffusion flux, \(D\) is the diffusion coefficient, and \(\frac{dC}{dx}\) is the concentration gradient over a distance \(x\)). The small cube has a shorter distance (\(5\ \mu m\)) but a lower surface - area - to - volume ratio (\(0.6\)) compared to the smaller sphere (\(0.5\)). The lower surface - area - to - volume ratio of the cube means less membrane for oxygen entry per unit volume. So, the smaller sphere is the best as it combines a relatively high surface - area - to - volume ratio (for good nutrient entry) and a relatively short diffusion distance.

Answer:

A. Smaller sphere, because it allows the most rapid movement of nutrients from cell membrane to cell center