The arc length of the given sector is; S = 15.7 km
How to find the length of an arc?
From the given sector of the circle we are given that;
radius; r = 10 km
Angle subtended at the center; θ = 90°
Now, formula for arc length of a sector is;
S = rθ
where
r is the radius
θ is the angle measured in radians
Now, our angle 90 degrees in radians is;
90 degrees = π * 90/180 = π/2
Thus;
S = 10 * π/2
S = 10 * 3.14/2
S = 15.7 km
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