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Thus, the area of the dome is $ oxed{\dfrac{\pi s^2}{3}} $.
Question: A cartographer uses satellite data to map a circular forest reserve. A straight river crosses the reserve forming a chord of length 14 km, and the shortest distance from the forest’s center to the river is 5 km. What is the area of the forest in square kilometers?
Solution: Let $ r $ be the radius of the forest. The chord length is 14 km, so half is 7 km. The perpendicular distance from the center to the chord is 5 km. Using the Pythagorean Theorem:

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