Question 1178405
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The side length of the cube is   a = {{{root(3,2744)}}} = 14 cm.


The diameters of the sphere is  d = {{{sqrt(14^2+14^2+14^2)}}} = {{{14*sqrt(3)}}} cm.


The radius of the sphere is  r = {{{7*sqrt(3)}}} cm.



The volume of the sphere is  {{{(4/3)*pi*r^3}}} = {{{(4/3)*3.14*(7*sqrt(3))^3}}} = 7461.81 cm^3



The volume of the non-occupied part of the sphere is


    7461.81 - 2744 = 4717.81 cm^3.      <U>ANSWER</U>
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Solved.