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)?

I think i've stumbled on another more simple method of calculating the radius of the smaller circle firstly work out the length of the line that connects two diagonal corners, then divide this by 4 (centres of the circles intersect this line into quarters), then subtract 1 (initial radius unit)

(4^2)*3 = 48
Sqroot 48 = 6.9282032302755
6.9282032302755/4 = 1.7320508075688772
1.7320508075688772 - 1 = 0.7320508075688772

Posted by Phil on 2004-02-09 19:12:09