From: John K Clark (jonkc@att.net)
Date: Mon Oct 28 2002 - 22:05:51 MST
> John K Clark wrote:
> > A cylindrical hole six inches long is drilled straight through
> > the center of a solid sphere. What is the volume remaining in
> > the sphere?
spike66" <spike66@attbi.comWrote:
> Cooooool! Cool question John! I get 4*pi cubic
> inches, regardless of the diameter of the sphere.
> I did it with only one integral using cylindrical
> shells. {8-] spike
Actually the answer is that the remaining material is always equal to the
volume of a 6 inch sphere [ (4/3)*pi*r^3 where r =3]. You can find the
derivation from first principles at
http://mathforum.org/library/drmath/view/55631.html but you can also get the
answer easier if you're willing to cheat a little. If you assume the
question has a answer then it must be true regardless of the diameter of the
hole drilled, even if the diameter is zero, hence the remaining volume must
simply be that of a 6 inch sphere.
I also found that some unknown great man has asked the question more
poetically.
Old Boniface he took his cheer,
Then he bored a hole through a solid sphere,
Clear through the center, straight and strong,
And the hole was just six inches long.
Now tell me, when the end was gained,
What volume in the sphere remained?
Sounds like I haven't told enough,
But I have, and the answer isn't tough!
John K Clark jonkc@att.net
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