The diagonal of the square will be the diameter of the circle.
The radius is 1, so the diameter is 2.
Let x= one side of Square, So the area will be $x^{2}$
Using the Pythagorean theorem (and knowing that all sides of a square are congruent) we get:
$x^{2} $+ $x^{2}$ = $2^{2}$
$2x^{2}$ = 4
Area of Square($x^{2}$) = 2
Hence,Option(B)2 is the correct choice.