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Assume that an average cell has a diameter of 7 micrometers ​(7x 10(6) meter), which means it has a volume of 200 cubic micrometers. How many cells are there in a cubic​ centimeter?

Guest Sep 28, 2017
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We want to know... how many cells are there in a cubic​ centimeter?

 

That is.....how many  200 cubic micrometers  are there in a cubic centimeter?

 

We want to know...what is   \(\frac{1\,\text{ cubic centimeter}}{200\,\text{ cubic micrometers}}\)    ?

 

First let's convert 200 cubic micrometers into cubic centimeters.

 

1 meter  =  1 · 102 centimeters  =  1 · 106 micrometers

 

1 · 102 cm    =    1 · 106 µm       Divide both sides by  106 .
1 · 102 / 106 cm = 1 µm    
1 · 10-4 cm = 1 µm   Cube both sides.
(1 · 10-4 cm)3 = (1 µm)3    
1 · 10-12 cm3 = 1 µm3   Multiply both sides by  200 .
200 · 10-12 cm3 = 200 µm3    
2 · 10-10 cm3 = 200 µm3    

 

So.....

 

\(\frac{1\,\text{ cubic centimeter}}{200\,\text{ cubic micrometers}}\,=\,\frac{1\,\text{ cubic centimeter}}{2 \cdot 10^{-10}\,\text{ cubic centimeters}}\,=\,\frac{1}{2\cdot10^{-10}}\,=\,5\cdot10^9\)

hectictar  Sep 28, 2017

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