what is the surface area to volume ratio of a cell that is 100 micrometers on one side? Is this ratio good for a cell or not? Why?

Answers

Answer 1
1.For a cell that is 100 micrometers on one side, 
Let assume that the cell is cuboidal in shape,
surface area of one side = 100 * 100 = 10000 micrometers
There are six sides to a cube, 
Thus, total surface area = 6*1000 = 6000
Volume = 100 * 100 *100 = 1,000,000
Surface to volume ratio = 6000/1000000
0.006.
Therefore, the surface area to volume ration for the cell is 0.006.
2. This surface area to volume ratio is not good for the cell. This is because, the surface area to volume ratio is too small.
In order for a cell to effectively obtain the nutrients that it needs through the diffusion process, the ratio of the surface area of the cell to its volume must be high, if not the cell will not be able to get adequate nutrients for its survival and this may lead to its death. Cells divides continuously majorly because they want to maintain high surface area to volume ratio of their cells. A cell that is too big will have low surface area to volume ratio.


Answer 2

Final answer:

The surface area to volume ratio for a cell with 100 micrometer sides is 0.06, which is considered low and not conducive to efficient exchange of materials with the environment, potentially impairing cell function due to insufficient nutrient supply and waste removal.

Explanation:

The surface area to volume ratio of a cell that is 100 micrometers on one side can be calculated by first finding the surface area (SA) and the volume (V). The surface area is SA = 6 × (side length)² and the volume is V = (side length)³. Since the side length is given as 100 micrometers, the surface area is 6 × (100 µm)² = 60,000 µm² and the volume is (100 µm)³ = 1,000,000 µm³. Thus, the surface area to volume ratio is 60,000 µm² / 1,000,000 µm³ = 0.06. This ratio means that the cell has 0.06 square micrometers of surface area per cubic micrometer of volume.

In terms of cell biology, a higher surface area to volume ratio is typically considered better because it allows for more efficient diffusion of substances in and out of the cell. The calculated ratio of 0.06 is relatively low, suggesting that if a real cell had this ratio, it may not be able to efficiently exchange materials with its environment. Consequently, such a low ratio could impair cell function, as the cell would have difficulty supplying enough nutrients and expelling waste quickly enough for its large volume.


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Hello There!

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Hope This Helps You!
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