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Home » = 4 eginvmatrix 9 & -18 \ -18 & 20 \endvmatrix - Coaching Toolbox

= 4 eginvmatrix 9 & -18 \ -18 & 20 \endvmatrix - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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

📌 e = \sqrt[3]{96} = \sqrt[3]{8 \cdot 12} = 2\sqrt[3]{12}

📌 The edge length is $ \boxed{2\sqrt[3]{12}} $ cm.

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