Equatorial Belt.

4. Equatorial belt

A snug-fitting belt is placed around the Earth's equator.  Suppose you added an extra 1 meter of length to the belt, held it at a point, and lifted until all the slack was gone.  How high above the Earth's surface would you then be?  That is, find h in the diagram below.

Assume that the Earth is a perfect sphere of radius 6400 km, and that the belt material does not stretch.  An approximate solution is acceptable.

A:

For this calculation we need PiR^2

As we know 1 meter is 'h' we calculate 'r' by adding 'h' into 'r', basically we calculate, how many 'h' go into 'r' and add 1. So, I would approximate 6, so the radius is 6400, so we do the following sum.

6+1 (7)*3.14{pi for arguments sake}^2 =

2*3.14 = 6.28
2*6.28 = 12.56 {4}
2*12.56 = 25.12 {8}
25.12 - 3.14 = 21.98 {7}

21.98 * 21.98 =
Approx 22*22 = 484

Precise 0.2 * 21.98 =
or 21.98/5 = 4.396
8.792
13.188
17.474
21.98

484 - 4.396 = 479.604 {Precise Answer}

Think this is incorrect?

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Thanks.