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But for now, skip and generate a valid one. - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A = \pi R^2 = \pi \left( rac{s\sqrt{3}}{3}

📌 ight)^2 = \pi \cdot rac{3s^2}{9} = rac{\pi s^2}{3}

📌 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 forestâs 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:

📌 r^2 = 5^2 + 7^2 = 25 + 49 = 74

📌 Thus, the area of the forest is:

📌 \pi r^2 = 74\pi

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