Question 1125545
Surface area of a sphere = {{{ 4(pi)r^2 }}}   where r=radius
Surface area of a cube = {{{ 6a^2 }}}   where a=length of one side <br>

We need to relate r to a.  Since the sphere just touches the sides of the cube, a = 2r.

So now we can write   {{{ 4(pi)r^2 / 6(2r)^2 }}} =  {{{ 4(pi)r^2 / (24r^2) }}} = {{{ pi / 6 }}}

{{{ pi/6 }}} is approximately 0.5236   so  we can write the sphere has a surface area that is about <b>52% </b> of the surface area of the cube.