Question 1129803
If s is the length of the sides of the cube, then  {{{ r[sphere] = s*sqrt(3)/2 }}}  <—<<< r is 1/2 the diagonal length of the cube, which is  {{{ sqrt(s^2 + s^2 + s^2) }}}

a) {{{ r[sphere] = 2sqrt(3) cm}}}  or  about 3.464cm <br>

b)  Because r can be expressed as a function of s,  the ratios can be found in general (the {{{s^3}}} will cancel), without the need for a specific radius:
{{{ V[cube] = s^3 }}}
{{{ V[sphere] = (4/3)(pi)(r^3)  = (4/3)(pi)(s*sqrt(3)/2)^3 }}}<br>

{{{ V[sphere]/V[cube] = ((4/3)(pi)cross(s^3)(sqrt(3)/2)^3) / cross(s^3) =  (sqrt(3)/2)pi }}} or about 2.7207.