棱长为2√3的正四面体内切一球,然后在它四个顶点的空隙处各放入一个小球,则这些小球的最大半径为多少.

V=(2*3^1/2)^2*sin60*1/2*2*2^1/2=6*6^1/2
V/4=(2*3^1/2)^2*sin60*r*1/2
r=√2/2
h=3
x=h-2r=3-√2
(3-√2)/(3-√2/2)=R/r
((3-√2)*√2/2)/(3-√2/2)=R
(3*√2-2)/(6-√2)=R