How to find surface area/volume ratio of a cell?Pl explain with examples.


The surface area to volume ratio of a cell is the surface area of a cell divided by it's volume.

Since a cell is generally spherical in shape, we will find the surface area of the cell as 4πr2 
(where r = radius of cell)

It's volume will be: 43πr3

Thus, the surface area to volume ratio of a cell is: 

The surface area to volume ratio of cells generally decreases as cells get larger, making the exchange of resources, wastes and heat more and more difficult.  

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if you know the radius caluculate it like this
with r the radius of the cell

The next question: How would you measure this radius in the first place?

Most cells are spherical in suspension. That is, when they are freely suspended in a liquid medium, they exert the same forces in all directions, thus making them spherical.

You can take a picture in a camera equipped microscope at a known magnification and use a scale bar to measure cell radius. There are also methods to automate this through image processing

Note: This rule however does not apply to plant cells (rigid cell wall), RBCs (flattened) or many bacterial cells that retain a different shape. In these cases, you can approximate the cell to be a cylinder, disc, cuboid, etc and use known formulae, or if you have access to a confocal microscope, you can get 'slices' very much like a CT scan, and you can build a 3D model of the cell from it. Calculation of surface area and volume shouldn't be difficult after this.
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