Question 1187361
# 1187361  (KMST)
The human body contains approx. 30 trillion red blood cells. If these cells were placed tightly together, 
they would fit into a cube approx. 5 in. on each edge.
1) Determine outside surface of cube in sq. yds.
2)If the outside surface of cube was divided into 30 trillion pieces, determine outside surface in sq. yds.
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        In this post, the problem is formulated incorrectly.


        It is also incorrectly interpreted, incorrectly treated and incorrectly solved by the other tutor.


        The meaning of the problem is totally different, and after proper solution

        the answer will shock you, because it will disclose absolutely unexpected phenomena.



        The correct formulation is (and should be) as follows


                    The human body contains approx. 30 trillion red blood cells. If these cells were placed tightly together, 

                    they would fit into a cube approx. 5 in. on each edge.

                        1) Determine outside surface area of cube in sq. yds.

                        2) If the volume of cube was divided into 30 trillion pieces/(small cubes), determine their total 

                               outside surface area in sq. yds.



      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U> S  O  L  U  T  I  O  N</U>,  &nbsp;&nbsp;step by step



<pre>
(1)  surface area of the cube with the side 5 inches is  {{{6*5^2}}} = 6*25 = 150 square inches.

     It is the same as  {{{150/((3*12)^2)}}} = {{{150/1296}}} = 0.11574 sq. yards (approximately).



(2)  Now we are going to divide the 5x5x5-inches cube into 30 trillions smal cubes. 

         30 trillions = {{{30*10^12}}}.


     To find the linear size of small cube, we should divide 5 inches by  {{{root(3,30*10^12)}}} = 31072.325.

     By doing it, we get the size of small cube  s = {{{5/31072.325}}} = 0.000160915 inches.


     Then the surface area of this small cube is  {{{6s^2}}}  square inches.  

     It is very small area - - - but we have 30 trillions such small cubes,
     so, to get the total surface area of these 30 trillions small cubes,
     we should multiply  {{{6s^2}}}  by {{{30*10^12}}}.


     By doing it, we get for the total surface area the value

        {{{6*0.000160915^2*30*10^12}}} = 4660848.759 square inches,


     which is the same as  {{{4660848.759/((3*12)^2)}}} = 3596.333919 square yards.


Now the two values for the surface area to compare are  0.11574 square yards from part (1)
and  3596.3 square yards from my last calculation.


It tells us that the surface area of the red blood cells in dispersed state (as it is in the live human body)
is approximately 35000 times greater than the surface area of the 5x5x5-inches cube.


It is that unexpected phenomena which I pointed at the beginning of my post,
and it explains and discloses the fact that dispersed red blood cells distribute oxygen very effectively 
in the lungs and in all human's body.


These facts are of common knowledge.
I learned it in my 12 - 13 - 14 years, reading Children Encyclopedia on Biology.


I think that it should be clear to an analytical chemist @KMST as 2 x 2 x 2 = 8.
</pre>

Solved to satisfy your curiosity.