Question

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.

Answer 1

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