Final answer:
No, dividing the cell into 125 cells with a total volume of 1,000,000 μm3 does not ensure survival, as the resulting surface area/volume ratio is 0.3, which is less than the required ratio of at least 3.
Step-by-step explanation:
The question asks whether dividing a cell into 125 cells with a total volume of 1,000,000 μm3 would ensure a surface area/volume ratio of at least 3, a ratio needed for cell survival. If we analyze a single cell from the 125 cells, each cell would have a volume of 1,000,000 μm³=/125 = 8,000 μm³. To calculate the surface area of one of these cells, let's assume they are cubic for simplicity.
The cube root of 8,000 μm³ gives an approximate edge length of 20 μm. The surface area for a cube is 6 × (edge length)2, so the surface area of one cell is 6 × 202 = 2,400 μm². The surface area to volume ratio for one cell is then 2,400 μm² / 8,000 μm³ = 0.3. This is significantly less than 3, indicating that dividing the original cell into 125 cells with the described volume does not ensure survival based on the necessary ratio. Therefore, the answer is b. No, because the surface area/volume ratio is less than 3.