Question 1108536
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<pre>
If "s" is the cube's side length, then the cube's longest 3D diagonal is {{{sqrt(3s^2)}}} = {{{s*sqrt(3)}}}.


At the same time, this longest diagonal is the DIAMETER of the sphere:

{{{s*sqrt(3)}}} = 2r.


Therefore,  {{{r/s}}} = {{{sqrt(3)/2}}}.
</pre>

Solved.