I answered this question a few days ago, and at that time the dimensions of the water cases were accidentally given in feet instead of inches. I can see that's been coorected now.
I'll go over the solution again, and give some answers on the perimeter and area.
First, the volume of a case: 10.2*15.1*8.3=1,278.366cu in=0.74cu ft (approx).
Each crate has three dimensions, but the way to lay out the crates to circumscribe the earth with the minimum number of crates is by their lengths.
2.6*10^9 (2.6 billion) laid lengthwise is 3.926*10^10 inches=619,633.8 miles=24.88 equators approx.
The volume of that number of cases is 2.6*10^9*1,278.366=3.32375*10^12cu in=1.92347 billion cu ft=0.01307 cu miles.
The perimeter of the cases if laid in a long line with the bottles upright would be 2*(3.926*10^10+8.3)in=7.852*10^10in=1,239,267.7 miles approx (the case width is so small in comparison the length of all those crates can be ignored).
The surface area would be the sum of the areas of the three visible sides. We can ignore the areas of the exposed ends of the first and last cases compared to the rest of the surface areas.
Total exposed surface areas: 2.6*10^9(2*15.1*10.2+15.1*8.3)=2.93*10^21 sq in=2.034*10^19 sq ft=7.30*10^11 sq miles.