Is it wise to buy commercial-size toilet paper?
The Sunday Nation
Nairobi,
14 July 2013
You know that times are hard when people start economising on toilet paper! Joseph Wainaina is doing exactly that. He says that, like everybody else, he has been buy the normal size tissue rolls for home use but some one offered him a “commercial sized” one recently – the large type found in hotel or shopping mall toilets.
Joseph writes: “The street trader said that the commercial spool is 100m long while the domestic ones are only 10m. When I looked at it, it didn’t look like it was ten times larger than the usual roll. May be that’s why the price was just four times that of the normal size. Can you figure out if this is a good deal?”
On reading Joseph’s email, I went to the supermarkets with a ruler to measure the sizes of toilet paper – the things that readers make me do! Anyway, here are the results:
The regular domestic roll measures about 10.5cm in diameter and it is wound on a spool that is 4.5cm wide. Closer inspection revealed some additional information. The toilet paper is divided into 200 sheets each measuring 12.5cm in length. Therefore, the complete roll must be 2,500cm long (12.5cm x 200 sheets); that is, 25m.
Now this is exactly a quarter of the length of the commercial roll (100m divided by 4 is equal to 25m). So, it makes perfect sense that the price of the larger roll is four times that of the smaller one – Joseph isn’t getting any price advantage!
What remains now is to establish whether the 100m claim is true. To find out, I also measured the diameter of the commercial roll. This came to about 19cm. Since these diameters depend very much on how tightly the rolls are wound, I was careful to take measurements on the same brand of tissue.
At first sight, there seems to be something wrong: 19cm is definitely not near four times the 10.5cm of the domestic roll. What’s going on?
The problem is that humans are accustomed to direct linear proportions, but in this case, the relationship we want is between areas – not diameters. That is, the flat surfaces of the rolls.
To get the area covered by the tissue, we subtract that of the spool from that of the whole roll. The formula is the well-known pi-r-squared.
The radius the domestic roll is 5.25cm (half of 10.5cm) thus the flat area is 86.6sq-cm. For the spool, the answer comes to 15.9sq-cm. Therefore the part covered by the tissue is 70.7sq-cm.
In the commercial roll, the radius is 9.5cm (half of 19cm); so the flat surface is 283.5sq-cm. The spool is the same size as that on the domestic type, that is, 15.9sq-cm. Thus the area covers by the tissue is 267.6sq-cm.
And now the final test: what is 267.6 divided by 70.7? The answer is about 3.8. Now 3.8 is close enough to four - the ratio of the lengths of the two rolls. Therefore, I don’t doubt the manufacturer’s claim – the commercial roll is four times as long as the domestic one.
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