A seven pack is better than a six-pack
The Sunday Nation
Nairobi,
20 May 2012
The six-pack is a popular packaging style for canned and bottled drinks. It comprises six cans (or bottles) arranged in a 3 x 2 pattern. This is an interesting arrangement because rectangular grids are not appropriate for circular objects: It is like attempting to fit “round pegs into square holes”!
So, is there a better arrangement? To find out, let’s do a practical activity.
You will need ten coins of the same size. Now put one of them on a flat table surface. Next, place a second coin touching the first one. Then put the third one touching the other two. So now you have three coins all touching one another: what shape does this arrangement have?
It’s a triangle.
Let’s continue: place the fourth coin touching coin 1 and 3; then the fifth one touching number 1 and 4. Continue arranging this way until coin 1 is completely surrounded. How many coins are on the table so far?
They should be seven.
What is the shape of this arrangement? One might be tempted to call it circular because outer coins are arranged “around” central one. That, however, would be incorrect. The coins actually fall into a six-sided pattern – a hexagon – with two coins on each side. But don’t forget that there are seven coins in total.
If soda bottles were arranged in this manner, then we would have a seven-pack instead of a six-pack. But why would any manufacturer bother to put them this way? Well, I can think of at least one reason: cost of packaging. Let me explain…
A plastic soda bottle measures about 6cm in diameter. Suppose six bottles are arranged inside a rectangular carton box in the usual 3 x 2 configuration. The dimensions of the box will be about 18cm x 12cm. Therefore, they are sitting on a base whose total area is 216sq-cm.
Since there are six bottles, this comes to an average of 36sq-cm per bottle.
Calculating the base area needed for a seven-pack hexagonal arrangement is not a straightforward matter; but it turns out to be about 233sq-cm for the 6cm soda bottles. This works down to about 33sq-cm per bottle.
Clearly, six-pack needs about 9 per cent more packaging material at the base of the carton. This might appear small, but that’s just part of the package: the carton also has sides.
In the case of the 3 x 2 six-pack, the total length around the carton is 60cm (18+12+18+12). The sides of hexagonal seven-pack are all equal and each measures about 9.5cm; that is a total of 57cm – this is smaller but it surrounds more bottles!
Again working out the amount per bottle, it turns out that the seven-pack needs 8.1cm and the six-pack 10cm – another 23 per cent extra for the rectangular packing.
With such clear savings on packaging materials, isn’t it surprising that manufacturers are still attempting to fit round pegs into square holes?
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