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.

Volume = Pi*(Radius)^2*(Height)

[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:

Volume = (4/3)*(Pi)*(Radius)^3

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