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Home » $ 19a + 5b + c = 16 $ - Groen Casting

$ 19a + 5b + c = 16 $ - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The altitude corresponding to a side is $ h = \frac{2A}{\text{side}} $. The longest altitude corresponds to the shortest side, which is 13 m:

📌 h_{\text{longest}} = \frac{2 \cdot 84}{13} = \frac{168}{13} \approx 12.923

📌 But we compute exactly:

📌 h_{\text{longest}} = \frac{168}{13}

📌 Thus, the length of the longest altitude is $\boxed{\dfrac{168}{13}}$ meters.

📌 Question: A Martian colony is built inside a hemispherical dome with radius $ R $. A cylindrical habitat module of radius $ \frac{R}{2} $ and height $ R $ is inscribed within the dome. What is the ratio of the volume of the cylinder to the volume of the hemisphere?

📌 Solution: The volume of the hemisphere is:

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