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### Copies of U.S. on Surface of Earth

```
Date: 11/07/2001 at 21:20:25
From: Nathan
Subject: Surface area

I need to determine the number of identical copies of the continental
United States that would fit on the surface of the Earth.
```

```
Date: 11/08/2001 at 12:12:28
From: Doctor Ian
Subject: Re: Surface area

Hi Nathan,

That's a tough question! The continental United States (CUS) has an
irregular shape, so it's not as if you can just divide the surface
area of the earth by the surface area of the CUS to get the number of
copies. That would give you an approximation, but it would be too
large. (Do you see why?)

The most accurate way to solve this problem would be to get a globe,
cut out copies of the CUS at the appropriate scale, and see how many
you can fit onto the globe.

As another approximation, you might try this: Determine the smallest
rectangle that would contain the CUS. It will have some height and
width. If you divide half the circumference of the globe by this
height, you'll get a number that will be the number of 'bands' of
rectangles that you could wrap around the globe.

Figure out the circumference of the bottom of each band; and divide
that by the width of the rectangle. That would tell you how many
copies you could fit into that band. (You can use symmetry here - once
you've done this for the northern hemisphere, you can double the
result to take the southern hemisphere into account.)

This approximation would be too small. (Do you see why?) But you could
just say that the answer must lie somewhere between the two
approximations.

Does this help?

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

```
Date: 11/19/2001 at 20:35:57
From: Nathan
Subject: Re: Surface area

It does help. Thanks a lot.
```
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry

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