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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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The text passage contains a question from a 7th grader about finding the volume of a trash bag and a detailed response from Dr. Ethan providing both experimental and mathematical approaches to solve the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search
user
The text passage contains a question from a 7th grader about finding the volume of a trash bag and a detailed response from Dr. Ethan providing both experimental and mathematical approaches to solve the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER