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

Comments: (
You must be logged in to post comments.)