Copies of U.S. on Surface of EarthDate: 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. |
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