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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 
Associated Topics:
Elementary Measurement
Middle School Measurement

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