Imagine the earth is a huge sphere with a belt around it. A new belt is made 20 ft longer than the original. Imagine they are concentric circles (having the same center). How far away are these two belts from each other??
2007-01-31 08:37:47 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The diameter of the earth is listed at 12,756.3 km at the equator.
12,756.3 km * 1000 m/km * 100 cm/m /2.54 cm/inch / 12 inch/foot = 41,851,377 feet. The circumference of a circle is given by 2 * pi * r, which is the same as diameter * pi. Therefore, a belt around the equator would be (41,851,377 feet * 3.14159...) = 131,479,982 feet long. If you increase that length by 20 feet to 131480002 feet, then you get a new diameter of (131480002 / pi) = 41,851,384, which is 7 feet more than before. Remember we've calculated the difference in diameters, so the distance seperating the belts is half this number - 3.5 feet.
2007-01-31 08:53:43 · answer #1 · answered by Grizzly B 3 · 0⤊ 0⤋
Argh. Okay, let's say the earth has radius R. So it's circumference is 2pi*R. This new belt has circumference 2pi*R+20. It's radius must then be (2pi*R+20)/2pi, or R+10/pi. Thus the belts are 10/pi ft apart.
2007-01-31 16:45:35 · answer #2 · answered by astazangasta 5 · 0⤊ 0⤋
C = 2*pi*r
dC/dr = 2*pi
dr = dC/2*pi
dr = 20/2*pi = 3.183 feet approximately
2007-01-31 16:48:50 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋