The circles are the bottoms of the bottles.  The left front corner looks like
this.  We are looking down upon the bottles in the box.



There are 100 bottles on the 1st row, 99 on the 2nd row, 100 on the 3rd row, 
etc.  So between the front side of the box and the green line, there are 299 
bottles.

The two red triangles are 30-60-90 right triangles, each with vertical sides 
.  It's 2 more radii (one diameter) from the side of the box to
the green line, so the distance from the side of the box to the green line is 
 cm.  We divide that into 1000 and get 36.6+.  

So 36 times 299 bottles gives us 10764 bottles up to  cm.
So there are  or about 16.5 cm. left from the green line
to the left back side of the box.

 

So there is only room enough for 1 more row of 99 bottles, or 10764+99=10863
bottles.  But if they didn't have to each have their centers 60o apart, 
we could easily squeeze in a few more bottles. Maybe another tutor will do a
better job that I have here.

Edwin