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How do I calculate the surface-area- to-volume ratio for a square or cube cell that is 3 mm each side?
The answer to your question is below along with a general formula so you can see where the answer comes from.
The formula for the volume of a cube with side length L is L3
The formula for the surface area comes from finding the area of one side of the cube and multiplying that by 6 since there are 6 sides. The area of one side is L2 so
the surface area is 6L2 .
Now if we want ratio of surface area to volume for any cube, it would be 6L2 /L3
This simplifies to 6/L
So in the case of a cube with side length 3 mm it is 6/3 or 2.
Method 2 would be to find the surface area and volume for your cube only and then divide.
The volume is 33 and the surface area is 6(32 ) so the ratio of surface area to volume is
6(32 )/33 =2
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