The length of the arc is 1/4th of the circumference .
The circumference of any large circle is the length of the intersection of the sphere with any plane passing through its center. A meridian is a large circle that passes through a point called a pole. The shortest distance between any two locations on a sphere is called a geodesic. When calculating the circumference of this arc, we must first determine the fraction of the circumference. A center angle of radians is subtended by an arc.
We know, that an arc with a central angle of has a diameter of:
[tex]Arc=\frac{Angle}{360} (2\pi r)[/tex]
[tex]Arc=\frac{\pi }{2} /360 (2\pi r)[/tex]
[tex]Arc=\frac{90}{360} (2\pi r)[/tex]
[tex]Arc=\frac{90}{90(4)} (2\pi r)[/tex]
[tex]Arc=\frac{1}{4} (2\pi r)[/tex]
[tex]Arc=\frac{1}{4} (circumference)[/tex]
Hence, 1/4 of the circumference is the length of the arc.
Learn more about circumference here: brainly.com/question/20489969
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