3. Given a hemispherical bowl with a radius of 2 containing four smaller spheres each with a radius of $r$. The surfaces of the bowl and the spheres are smooth, and each smaller sphere is tangent to the plane of the bowl's rim. Then the value of $r$ is $\qquad$ .
Solve:
As shown in the figure, $A, B, C, D$ are the centers of four small spheres with radius $r$, $A E=$
$$
\begin{array}{l}
A A_{1}=r, A B=A_{1} B_{1}=2 r, \text { then } O A=2-r \\
\Rightarrow O A_{1}=\sqrt{4-4 r}=\sqrt{2} r \Rightarrow r^{2}+2 r-2=0 \\
\Rightarrow(r+1)^{2}=3 \Rightarrow r=\sqrt{3}-1 .
\end{array}
$$