
Bag Of Balls
Problem
Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and the next ball.

If the radii of the balls are 20 cm, 12 cm, and r cm respectively, what is the value of r?
Solution
Consider the following diagram.

Using similar triangles, (12 + r)/(12 r) = 32/8 = 4.
12 + r = 48
4r
5r = 36
r = 7.2 cm.
What if the radii of the three balls were 20 cm, r cm, and 10 cm?
If the top sphere has radius, x, and the bottom sphere has radius, y, find r in terms of x and y.
Problem ID: 139 (Dec 2003) Difficulty: 3 Star