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It seems surprising, but that steel belt, after a
meter is added to it (approximately a yard and four inches), will be
raised 15+ centimeters (approximately six inches) all the way around!
This is certainly high enough for a baseball to pass underneath.
Actually, the height the belt is raised on, is the same regardless of
how large the sphere is. It is easy to see why. When the belt is tight
around the sphere, it makes the circumference of a circle with a
radius that is the same as the radius of the sphere. As it is known
from plane geometry the circumference of a circle is equal to its
diameter (which is twice its radius) times pi. Pi is 3.14+. Therefore,
if the circumference of any circle is increased by one meter, the
diameter of the circle is increased by a trifle less than one-third of
a meter, or 31+ centimeters (a trifle more than a foot). This means,
of course, that the radius will increase by almost 15+ centimeters
(approximately six inches).
As it is shown in the illustration, this increase in radius is the
height that the belt will be raised from the sphere's surface. It will
be exactly the same, 15+ centimeters (almost six inches), regardless
of whether the sphere be the size of the sun, of the earth or of an
orange! |
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