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### Cylinders and Elephants

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Date: 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?
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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

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/
```
Associated Topics:
Elementary Geometry
Elementary Three-Dimensional Geometry

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