AMC 10 Step by Step
2003 AMC 10BProblem 17P16-20~2 minPrint

An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies 75%75\% of the volume of the frozen ice cream. What is the ratio of the cone's height to its radius? (Note: a cone with radius rr and height hh has volume πr2h/3\pi r^2 h / 3 and a sphere with radius rr has volume 4πr3/34 \pi r^3 / 3 .)

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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.