There are two spherical balls, each of radius 100 cm., lying on a perfectly horizontal floor and touching each other.
What is the diameter of the largest ball that can pass through the gap between the spheres and the floor ?

The line joining the centre of one of the large spheres with the small sphere forms a hypotenuse of length R + r with the other two sides of length R and R - r. Therefore:

R^2 + (R - r)^2 = (R + r)^2
2R^2 + r^2 - 2Rr = R^2 + r^2 + 2Rr
R^2 = 4Rr
r = R/4 = 25
diameter = 50

Posted by retiarius on 2003-09-24 09:52:27