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Many Marbles Mystery (Posted on 2005-06-29) Difficulty: 3 of 5
Five marbles of descending sizes are placed in a conical funnel. Each marble is in contact with the adjacent marble(s). Also, each marble is in contact all around the funnel wall.

If the smallest marble has a radius of 8mm, and the largest marble has a radius of 18mm, what is the radius of the middle marble?

Bonus question, suggested by "Juggler": what's the angle of the funnel walls?

See The Solution Submitted by Old Original Oskar!    
Rating: 4.0000 (2 votes)

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Solution The basic question. | Comment 1 of 4
The ratio of the radius of one marble to that of the next will be the same for each marble because of the similarity.  There are four steps for a total ratio of 18/8.  The middle marble will have gone through two of these steps.  So its radius is 8 * sqrt(18/8) = 12 mm.
  Posted by Charlie on 2005-06-29 20:48:40
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