Sphere Cube (Posted on 2004-02-09)

You may find this problem similar.

In a cube of side 4, I pack eight spheres of unit radius.

What is the largest sphere I can place in the center (such that it doesn't overlap any of the other spheres)?

	Submitted by SilverKnight
Rating: 3.0000 (5 votes)
Solution:	(Hide)
Think of a smaller cube, with vertices at each sphere's center. This smaller cube would have sides of 2. The long diagonal of this cube would then be 2√3, and this is also equal to twice the larger spheres' radius plus twice the smaller sphere's radius. Since twice the larger spheres' radius equals 2, the equation is 2√3 = 2 + 2(smaller sphere's radius), solving for the smaller sphere's radius shows the largest sphere that can be placed has radius √3 - 1

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-06-30 07:53:08
	No Subject	prashant	2004-03-29 08:00:56
	Less otherworldly	Dan Porter	2004-02-15 00:22:56
	re(3): another dimension	SilverKnight	2004-02-13 15:43:19
	re(2): another dimension	Tristan	2004-02-13 15:01:39
	re: another dimension	SilverKnight	2004-02-13 14:44:54
	another dimension	pleasance	2004-02-13 14:06:31
	my solution is completely wrong...:-)	John	2004-02-13 12:55:12
	a try	John	2004-02-13 12:24:38
	re(2): Different Sulution	York	2004-02-11 08:46:33
	i'll give it a swing	superfuous_nut	2004-02-10 18:54:03
	Stumbling merrily away	Phil	2004-02-09 19:12:09
	re: Different Sulution	Charlie	2004-02-09 11:19:57
	Different Sulution	York	2004-02-09 10:01:16
	solution	retiarius	2004-02-09 07:26:20
	More balls than most	Phil	2004-02-09 07:03:53