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HMMT 二月 2007 · 几何 · 第 5 题

HMMT February 2007 — Geometry — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 5 ] Five marbles of various sizes are placed in a conical funnel. Each marble is in contact with theadjacent marble(s). Also, each marble is in contact all around the funnel wall. The smallest marblehas a radius of 8, and the largest marble has a radius of 18. What is the radius of the middle marble?
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解析

英文解析

  1. [ 5 ] Five marbles of various sizes are placed in a conical funnel. Each marble is in contact with theadjacent marble(s). Also, each marble is in contact all around the funnel wall. The smallest marblehas a radius of 8, and the largest marble has a radius of 18. What is the radius of the middle marble?
    Answer: 12 . One can either go through all of the algebra, find the slope of the funnel wall and gofrom there to figure out the radius of the middle marble. Or one can notice that the answer will justbe the geometric mean of 18 and 8 which is 12.
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