The area of a sector of a circle is given by the formula:
A = (θ/360°) x πr²
where θ is the central angle of the sector in degrees and r is the radius of the circle.
In this case, the radius of the circle is given as 10 kilometers, and the central angle of the sector is 90°, so we can plug in these values to find the area of the sector:
A = (90°/360°) x π(10 km)²
A = (1/4) x π x 100 km²
A = (25/4)π km²
Therefore, the exact area of the sector bounded by a 90° arc of a circle with a radius of 10 kilometers is (25/4)π km², or approximately 19.63 km².