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ratio of volumes, truncated cone inscribed in sphere (2011 VWO Flanders MO p2)

Source:

August 7, 2020
ratiogeometry3D geometryspherecone

Problem Statement

The area of the ground plane of a truncated cone KK is four times as large as the surface of the top surface. A sphere BB is circumscribed in KK, that is to say that BB touches both the top surface and the base and the sides. Calculate ratio volume B:B : Volume KK.