Find the height

If  we connect the  centers of the  bottom three circles, we  will form an equilatersl triangle  with sides  = 4

The  height of this triangle   =  sqrt (3) / 2  *   side length

And, by symmetry, we have  two  of  these triangles......so their  combined  heights   =  sqrt (3) * side length  = 

4sqrt (3) cm

And  the other  part  of the  total  height is  formed  by 2  radii of a circle  =  2 * 2  = 4  cm

So....the total  height =   4 ( sqrt (3)  + 1)  cm  ≈   10.928 cm