Subj:.....Band
Around The Earth (S595b)
From: Yahoo! Answers on 6/14/2009


Source:
http://answers.yahoo.com/question
........./index?qid=20061218145859AA5G77v
Suppose
that the surface of the earth is smooth and spherical
and
that the distance around the equator is 25,500 miles. A
steel
band is made to fit tightly around the earth at the
equator,
then the band is cut and a piece of band 21 feet
long
is inserted. Then the separation of the band from the
earth
is spread evenly around the earth.
Can
you slide a piece of paper between the band and the earth?
Can
a mouse crawl between the band and the earth? Can a small
dog
go between the band and the earth? To the nearest inch,
what
will be the gap, all the way around, between the band and
the
earth's surface? (Use 3.14 as an approximate value of Pi)
THE SOLUTION
It doesn't matter
the size of the smooth sphere. Whether it
is a golf ball, basketball,
or the earth, if you increase the circumference of a circle by 21 feet,
the radius will increase
by 21 /2*Pi.
If we have to use Pi=3.14, then the radius is
increased by 3.3439
feet or 40.12 inches. That will be the
gap you will have
all around: 40 inches.
Here is the math:
In the original band
C = 2 pi r
so the original radius
was r = C
2 pi
In the new band its
length was C + 21, so C + 21 = 2 pi r
so the new radius
is r = C + 21
2 pi 2 pi
The new radius is
increased by 21/2pi or 3.3 feet or 40.1 inched.
The sheet of paper,
the mouse and the dog can all fit between
the band and the
earth because it is about 40 inches above the earth. 