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hilton garden inn newtown square pa 19073 - RTA

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 Solution: The shortest altitude corresponds to the longest side, which is $ 15 $ m. First, compute the area using Herons formula. The semiperimeter $ s $ is:

📌 The altitude $ h $ to the side of length 15 m is given by:

📌 Thus, the length of the shortest altitude is $ 11.2 $ meters.

📌 Question: An ancient Andean structure features a spherical dome of radius $ y $ and a supporting hemispherical foundation of radius $ 3y $. What is the ratio of the volume of the hemisphere to the volume of the sphere?

📌 Solution: The volume of the full sphere of radius $ y $ is:

📌 The volume of the hemisphere of radius $ 3y $ is half the volume of a sphere of radius $ 3y $:

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