Cylinders and Elephants

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?

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/