All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
Sphere Cube (Posted on 2004-02-09) Difficulty: 2 of 5
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)?

See The Solution Submitted by SilverKnight    
Rating: 3.0000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution More balls than most | Comment 1 of 16
firstly draw an imaginary cube using the centres of each of the spheres as the points on the box.
then use Pythagarus (i think) theory across one face to find the length of the diagonal. use this length as the base in a second triangle and use the measure of one edge as the second, calculate the third using said theory. subtract the length of to radii from this and the diameter of the sphere in the middle is given, half this to show radius

1. (R1+R2)^2+(R3+R4)^2=X^2
X=Diagonal length across centre of spheres on same face
2 (R5+R6)^2+X^2=Z^2
Z=length across centre of spheres directly opposite
3. (Z - (R1+R2))/2 = Radius of small sphere

placing in the figures

1. (1+1)^2+(1+1)^2=X^2
1a. Sqroot of X=2.8284271247
2. (1+1)^2+X^2 =Z^2
2a. Sqroot of Z=3.4641016151
3. (3.4641016151-(1+1))/2=0.732050807568 units of length for the radius of the centre sphere.

I have a feeling that there is an easier way to calculate this, but without an education i'm unable, i should have tried harder in school.

Phil
Edited on February 9, 2004, 7:11 am
  Posted by Phil on 2004-02-09 07:03:53
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (2)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (13)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information