A circumference with a radius of 1 meter and a central angle of 90 degrees represents a quarter of a circle. The formula for the circumference of a full circle is (C = 2\pi r), so for a radius of 1 meter, the full circumference is (2\pi \times 1 = 2\pi) meters. For a 90-degree angle, which is a quarter of the full circle, the length of the arc is ( \frac{1}{4} \times 2\pi = \frac{\pi}{2} ) meters.
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