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  ### Finding the Volume of a Trash Bag
  
  ```
  Date: 2/12/96 at 19:3:58
  From: tc2094
  Subject: find the volume of a trash bag
  
  Hi,
  
  I'm a 7th grader. How can you find the volume of a trash bag?
  I have to have a bag that is 3 cubic feet.  Can you help?
  ```
  
  ```
  Date: 2/13/96 at 17:7:11
  From: Doctor Ethan
  Subject: Re: find the volume of a trash bag
  
  Well, there are two basic approaches you can take to this:  an
  experimental approach and a mathematical approach.
  
  In the experimental approach, you could measure the volume of
  the bag by filling it with something the volume of which you can
  measure easily.  I would recommend water at first, but that could
  get _really heavy_ and break your trash bag.  You might go for
  something light, however, like the styrofoam peanuts people use
  to pack boxes.
  
  Once you've packed the bag, you can measure the volume of the
  stuff you put in it.  There are lots of other ways you could do this
  sort of test, and I'll leave that to your imagination.
  
  As for a mathematical approach, you might try one of several
  equations to approximate the volume, depending on how you're
  going to use it.
  
  For example, if you're going to use it to line a cylindrical trash
  can, you can find the trash can volume from.
  
  [I use x^2 to mean x squared, by the way.]
  
  If your trash bag is going to be closed at the end, you might be
  able to approximate the volume as if it were a sphere (though
  this is a very rough estimate).  You could blow the trash bag up
  much like a balloon and use the equation for the volume of a
  sphere:
  
  Personally, I would suggest the first approach since a trash bag
  can take on some very unusual shapes.  Finding their volumes
  might be possible, but it would require some very powerful math.
  
  -Doctor Ethan,  The Math Forum
  
  ```
  Associated Topics:
  Middle School Higher-Dimensional Geometry
  
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