# Can you visualize?

Geometry Level pending

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.

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