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2019 MPFG Problems/Problem 17

Revision as of 08:21, 11 August 2025 by Cassphe (talk | contribs) (Created page with "==Problem== Let <math>P</math> be a right prism whose two bases are equilateral triangles with side length <math>2</math>. The height of <math>P</math> is <math>2\sqrt{3}</mat...")
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Problem

Let $P$ be a right prism whose two bases are equilateral triangles with side length $2$. The height of $P$ is $2\sqrt{3}$. Let l be the line connecting the centroids of the bases. Remove the solid, keeping only the bases. Rotate one of the bases $180\circ$ about l. Let $T$ be the convex hull of the two current triangles. What is the volume of $T$?

Solution 1

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