Answer: about 5.73 inches off the ground
Note: the cable will need to be held up with vertical poles of this height so that a taut wire rope ring forms around the earth.
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Work Shown:
1 mile = 5280 ft
25000(1 mile) = 25000(5280 ft)
25,000 miles = 132,000,000 ft
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Let's find the radius of a circle that has circumference 132,000,000 ft
C = 2*pi*r
r = C/(2pi)
r = (132,000,000)/(2pi)
r = 21,008,452.4881301
The radius of the earth is approximately 21,008,452.4881301 ft
A more simplified view is that the radius is little over 21 million feet.
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Increase the value of C by 3 ft, so C = 132,000,003 now. Repeat the steps to get the larger radius to be...
r = C/(2pi)
r = (132,000,003)/(2pi)
r = 21,008,452.965595
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Subtract the two radius values
(larger radius) - (smaller radius)
(21,008,452.965595) - (21,008,452.4881301)
0.47746489569544
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This is less than a foot, so let's convert this to inches to see what comes up
Multiply by 12 to convert from feet to inches
0.47746489569544*12 = 5.72957874834529
This rounds to about 5.73 inches. Round the answer however you need to. Also, if you need me to convert to some other measurement, then let me know.
The height of the cable off the ground will be 5.73 inches high.
Circumference; C = 25,000 miles
From Conversion tables, we know that;
1 mile = 5280 ft
Thus;
25000 miles = 25000 × 5280
⇒ 132,000,000 ft
C = 2πr
Thus, radius is;
r = C/(2πr)
r = 132,000,000/(2π)
r = 21,008,452.48813 ft
Thus, [tex]C_{new}[/tex] = 132000003 ft
[tex]r_{new}[/tex] = 132000003/(2π)
[tex]r_{new}[/tex] = 21,008,452.965560
Thus;
Height of cable above the ground = [tex]r_{new}[/tex] - r
Height of cable above the ground = 21,008,452.96556 - 21,008,452.48813
Height of cable above the ground = 0.47743 ft
Converting to inches gives us;
Height of cable above the ground ≈ 5.73 inches.
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