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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