Solution :

It is given that, diameter of the circle =  side of a square

So, d = a

Given :

Area of the circle $= 64 \pi$ sq.cm.

        $\pi r^2$ sq.cm. $= 64 \pi$ sq.cm.

Therefore,       $r^2 = 64$

                             $r = ( 64 )^{1/2}$

                             $r = 8$

We know that $d = 2r$

So, $d = 2× 8$

       d = 16

Since $d = a, a = 16$

Area of the square $= a^2$ sq.cm.

                                  $= (16)^2$ sq.cm.

                                  $= 256$ sq.cm.

So, the correct option is 4). 256 sq.cm.