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.