8,9

Four spheres of radius 1 touch each other pairwise. Find the height of the cylinder containing these spheres such that three of them touch one base and the lateral surface, while the fourth touches the other base of the cylinder.
Let $O 1, O 2$, O3 and $O 4$ be the centers of the spheres, $H$ - the desired height of the cylinder. Consider the regular tetrahedron O1O2O3O4, with edge length 2. If $h$ is its height, then $h=2 \sqrt{\frac{2}{3}}$. Therefore,

$$
H=h+1+1=2 \sqrt{\frac{2}{3}}+2 \text {. }
$$

## Answer

$2 \sqrt{\frac{2}{3}}+2$