18 circles

which circle packing arrangement is the most compact?
an opportunity to use exact forms of trigonometric ratios

semicircle cutting

in a local factory one of the tasks was to cut out many semicircles, as lugs to be welded onto a drain hole cover

they cut these out with a laser in an obvious way:

is there a more efficient way to do this?

how might you compare these two and other arrangements?

there needed to be some distance between the shapes
otherwise the heat from the cutting process would warp the metal (say 2 mm gap)