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OA can be obtained according to Pythagorean theorem, then ∠ AOB = 90 can be obtained from the nature of rotation, and the answer can be obtained from the formula of sector area S sector =.

Solution: ∫ Every small square is a square with a side length of 1

∴OA=2，

∴S sector = = 2π.

So the answer is 2π.