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?

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