There is a perfect sphere of diameter 100 cms. resting up against a perfectly straight wall and a perfectly straight floor.
What is the diameter of the largest sphere that can pass through the gap between the wall, floor and the sphere ?

The'gap' created between a sphere of 2 units diameter and a perpendicular wall/floor can be easily found as root2 -1
So a sphere of 2 units can pass through a 'gap' of 2 + root2 -1 units
or root2 + 1
The sphere/gap ratio is therefore 2/r2 +1.
The maximum diameter sphere that can pass through a 'gap',X is
2X/r2+1
Here X is 50(r2-1) (50 times bigger than the 2 unit example)
So the answer is 100(r2-1)/r2 +1 = 17.157.....

Posted by Lee on 2003-09-15 03:00:54