Associated Topics || Dr. Math Home || Search Dr. Math

### Some Conversions are Impossible

```Date: 08/07/2006 at 23:32:02
From: Herman
Subject: convert square inch to cubic inch

How do I convert 567 square inches to cubic inches?

```

```
Date: 08/08/2006 at 12:48:10
From: Doctor Peterson
Subject: Re: convert square inch to cubic inch

Hi, Herman.

You don't.  Conversion means representing some quantity in terms of
different units; since square inches measure an area, and cubic
inches measure a volume, they can't represent the same quantity.  So
there's no way to convert one to the other.

But there are other things you can do.  Presumably you have some
situation in which some area is RELATED to some volume.  If we know
what that relationship is, we can find one from the other.

For example, if the area is the area of a garden, and the volume is
the amount of mulch to be spread over it 3 inches deep, then the
relationship is that the volume of the mulch (thought of as a cuboid
or a cylinder) is the base area times the height, so

V = Bh = (3 in) * (567 in^2) = 1701 in^3

Note that there is no way for me to do this without knowing, first,
the fact that the area is the base of a cylinder (the general
relationship), and, second, the height of that cylinder (additional
measurement relevant to that relationship).

Can you fill in the gaps in your question?

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Measurement
Middle School Measurement

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