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### Comparing Volume and Surface Area

```Date: 05/01/2002 at 12:13:58
From: Anonymous
Subject: Volume vs. surface area

Why is it that the surface area of a given rectangular solid can
sometimes be greater than the volume of that solid?
```

```
Date: 05/01/2002 at 13:09:40
From: Doctor Peterson
Subject: Re: Volume vs. surface area

Hi,

You can't really compare area and volume, since they use different
units. It's like asking why I am sometimes older than my weight, and
sometimes younger! (It depends on whether you use pounds or tons.)
You really can't say that 50 years is less than 160 pounds, and you
can't say that 50 cubic meters is less than 160 square meters.

Take a one-foot cube. Its volume is one cubic foot; its surface area
is 6 square feet, which is numerically greater. But if I use inches,
the volume is 12^3 = 1728 cubic inches, and its surface area is
6*12^2 = 864 square inches, which is numerically smaller. If one
object has its area sometimes smaller and sometimes greater than its
volume, depending only on the units I use, the comparison doesn't
mean anything, does it?

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```

```
Date: 05/03/2002 at 11:47:23
From: Anonymous
Subject: Volume vs. surface area

It makes sense the way you put it... Thank you!
```
Associated Topics:
High School Higher-Dimensional Geometry
Middle School Higher-Dimensional Geometry
Middle School Measurement

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