The New York Times’ Stephanie Clifford writes on efforts to reduce plastic in packaging:
Wal-Mart Stores, which has pledged to reduce its packaging by 5 percent between 2008 and 2013, [..] has made round hydrogen peroxide bottles into square ones to cut down on plastic use.
Anyone with 8th grade geometry knowledge should immediately stumble over that claim. It is contrary to the rather trivial fact that the region with a given area and minimal circumference is the circle.
Imagine a bottle holding 1,000 cubic units (units=inch, centimeter or whatever you like). Assume that it is ten units high. 1,000 cubic units divided by 10 units height gives a bottom (and top) area of 100 square units.
For the square packaging the total area of packaging material would be bottom+top+four times the side areas, in total 6 times 10 times 10 = 600 square units.
The radius of a circular bottom with an area of 100 square unit is the square root of (area divided by Pi). For a 100 square unit area the circle radius is r = 5.64 units. The area on the side of the bottle will be the circumference of the bottem circle times its high. The circumference of a circle is 2 times Pi times r here it is 35.44 units. The total area of the bottle side is then 10 times 35.44 units times 10 units. Adding bottom area, top area and side area gives a total surface area for the round 1,000 cubic units bottle as 554.4 square units.
As the thickness of the material for both bottles will be the same the square bottle will use 8% more plastic material than the round bottle.
Not a good way to “cut down on plastic use.”
In the retail business “revenue per square foot” is a major comparative performance parameter. If Wal Mart is indeed using square bottle instead of round ones it likely does so because the square bottles require less shelf space (and transport volume) than the round bottles. 100 square bottles with the size used above can be shelved on an area of 10,000 square units. The same shelf area will only hold a maximum of 82 round bottles of the same size.
Wal Mart is not concerned about plastic usage in packaging, it is concerned about revenue per square foot because that parameter is important to stock analysts and thereby its stock value.
For someone writing in a prime newspaper on retail business one would expect a better understanding of the basics of that business. But that would require some basic math knowledge. Something Stephanie Clifford seems to lack.