INFINITY SQUARES........

In the following picture, the smallest square has a side length of $1cm$ . The $four$ $vertexes$ are connected to the $dotted$ $circle$ below. The four sides of the $circle$ are then connected to the $second$ $square$ which is larger than the $first$ $square$ . (This is considered as one process.) At least how many time do we need to repeat this process to make the last square is larger than $1km^{2}$ ?