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- 13 + 1 = 19 - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The height of the trapezoid is $ \boxed{40} $ meters.

📌 Question: A bioinformatician is analyzing a 3D protein structure modeled as a regular tetrahedron with edge length $ e $. If the volume of the tetrahedron is $ 8\sqrt{2} $ cm³, what is the edge length $ e $?

📌 Solution: The volume $ V $ of a regular tetrahedron with edge length $ e $ is given by:

📌 V = \frac{e^3}{6\sqrt{2}}

📌 Set this equal to the given volume:

📌 \frac{e^3}{6\sqrt{2}} = 8\sqrt{2}

📌 Multiply both sides by $ 6\sqrt{2} $:

📌 e^3 = 8\sqrt{2} \cdot 6\sqrt{2} = 8 \cdot 6 \cdot 2 = 96

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