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MathNet 2010 — Part 06 Question 35

Math Olympiad Vault · MathNet 2010 — Part 06

Question 35

The metal cube with the surface of the $72~\mathrm{cm}^2$ is melted into a regular four-sided pyramid of the same volume, the length of which is equal to a third of the length of the body diagonal of the cube. What is the height of the pyramid?