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Geometry inequality on volume and area

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September 27, 2010
geometry3D geometryareaVolumegeometric inequalityIMO LonglistIMO Shortlist

Problem Statement

Prove that the volume VV and the lateral area SS of a right circular cone satisfy the inequality (6Vπ)2≤(2Sπ3)3\left( \frac{6V}{\pi}\right)^2 \leq \left( \frac{2S}{\pi \sqrt 3}\right)^3 When does equality occur?
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