Can you visualize?

Consider the $xyz$ space. Center of A sphere of radius (3) moves on $y-x=1,z=0$ .When its center is at a distance (2) from origin it stops moving.Then the planes $xz$ and $yz$ are made to rotate $\dfrac \pi8$ radian counter clockwise and clockwise respectively such that angle between them is $\dfrac\pi 4$ radians. The area of the cross section intersected by the 2 planes and sphere (ignoring negative (x,y) and including (-z) directions.) is given by $A$ .

Find $\lfloor A \rfloor$ .

(using calculator to find A is allowed).

Notation : $\lfloor \cdot \rfloor$ denotes the floor function .