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UKMT Senior Kangaroo, 2022

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

A cube is dissected into 6 pyramids by connecting a given point in the interior of the cube with each vertex of the cube, so that each face of the cube forms the base of a pyramid. The volumes of five of these pyramids are 200, 500, 1000, 1100 and 1400. What is the volume of the sixth pyramid?

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