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2014 AMC 10BProblem 23P21-25~9 minPrint
Solid GeometryCirclesQuadraticsApply an identity: SFFT, sum of squares, difference of cubes, VietaAdd construction lines/points (drop altitudes, extend segments, connect centers)Substitute to simplify (u = x+1/x, shifting, scaling)

A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is twice that of the sphere. What is the ratio of the radius of the bottom base of the truncated cone to the radius of the top base of the truncated cone?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.