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Home » Gogeta Gogeta: The Myth Behind the Fights You’ve Been Craving! - RTA

Gogeta Gogeta: The Myth Behind the Fights You’ve Been Craving! - RTA

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 5Question: A regular hexagon is inscribed in a circle of radius $ r $. What is the area of the hexagon in terms of $ r $?

📌 Solution: A regular hexagon can be divided into 6 equilateral triangles, each with side length equal to the radius $ r $ of the circumscribed circle. The area of one equilateral triangle with side length $ r $ is:

📌 Since the hexagon consists of 6 such triangles, the total area is:

📌 Solution: The inradius $ r $ of a right triangle can be expressed using the formula:

📌 This follows from the general formula for the inradius of a triangle:

📌 where $ A $ is the area and $ s $ is the semiperimeter. For a right triangle:

📌 Question: A sphere and a cube have equal surface areas. What is the ratio of the volume of the sphere to the volume of the cube?

📌 Solution: Let the surface area of both the sphere and cube be $ S $.

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