Cylinders and ElephantsDate: 05/30/97 at 00:47:44 From: philip brand Subject: Volume and shapes of containers Why are cans always manufactured as cylinders? I think it has something to do with the amount of volume it can hold. Are the volume of an animal and the surface area of its feet related? Date: 05/30/97 at 05:40:55 From: Doctor Mitteldorf Subject: Re: volume and shapes of containers Dear Phillip, It's true that when the shape of a can is being engineered, the ratio of the surface area to the volume is one of the things considered. However, there are other things to consider as well: attracting attention on the store shelf, for one. And ease of manufacture is another. On the subject of ease of manufacture: even though a cylindrical surface looks "curved" and we call it "curved", it can made from a flat piece of metal. Since rolled steel (or aluminum) comes in sheets, this is important. Imagine how much more complicated it would be to manufacture a sphere, which is curved in two dimensions, and for which you can't just start with a flat sheet. In fact, you have to start with a spherical piece of exactly the right radius. The foot size that an animal needs is proportional to its weight which is proportional to its volume, since almost all animals are roughly the density of water. If you just made a copy of a 1-foot cat the size of a ten-foot elephant, you'd find that the elephant weighed 1000 times as much but its feet were only 100 times the area. The feet wouldn't be able to hold the weight. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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