Question 1072412
The diagonal length of the box (7cm x 7cm side) must fit into the diameter of the circular opening.

Let d=minimum diameter

{{{ 2r =  d =  sqrt(7^2 + 7^2) }}}
{{{  d = 7*sqrt(2) }}}
{{{ d = 9.9cm }}}  (approx.)
            

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{{{drawing( 300, 300, -10,10,-10,10,
  grid( 1 ),
  circle( 0, 0, 4.97 ),
 
  line( -3.5, 3.5, 3.5,3.5 ),
  line(  3.5, 3.5, 3.5,-3.5 ),
  line( 3.5, -3.5, -3.5,-3.5 ),
  line( -3.5, -3.5, -3.5,3.5 ),
  line( 0,0, 3.5,3.5 ),
   locate( 2.2,2, r ) 
)}}}