Figure 1

Take a bead 5 inches high, and bore a hole through it
from north pole to south pole in such a way that the part
which remains is 4 inches high (measured lengthwise through
the hole).
Now take a bead 5 feet high, and bore a hole through it
in the same fashion, so that the part which remains is
also 4 inches high (you'll have to bore a very large hole).
Surprisingly, the volumes of the two "holey" beads are
now exactly the same! (In fact, the same
volume as a 4inch bead with no hole!)
Actually, it doesn't matter how big the bead is
that you start with...
you could have started with the Moon, and it would still
be true.
Presentation Suggestions:
Draw suggestive pictures!
The Math Behind the Fact:
You can assign the proof as a homework exercise in
multivariable calculus.
Cavalieri's principle might be helpful.
How to Cite this Page:
Su, Francis E., et al. "Holey Beads."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
