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From: ins_apmj@jhunix.UUCP (Patrick M Juola)
Newsgroups: net.puzzle
Subject: Re: The volume of the ring  (* SPOILER *) (not rot)
Message-ID: <1797@jhunix.UUCP>
Date: Thu, 6-Feb-86 17:56:52 EST
Article-I.D.: jhunix.1797
Posted: Thu Feb  6 17:56:52 1986
Date-Received: Tue, 11-Feb-86 03:23:52 EST
References: <794@alberta.UUCP>
Reply-To: ins_apmj@jhunix.ARPA (Patrick M Juola)
Distribution: net
Organization: Johns Hopkins Univ. Computing Ctr.
Lines: 44
Summary: Here is the solution with explanation

[munch munch]

Sometime I'm going to have to have someone show me how to rot13....












In article <794@alberta.UUCP> jim@alberta.UUCP writes:
>
>A ring is made by drilling a cylindrical hole through the center of a
>sphere.  The hole is 1 cm. long.  What is the volume of the ring?
>
>	Jim Easton (..!alberta!jim)

Assumption number 1 -- the problem is solvable.  If it isn't, I would have
rude words for the author.  This means that there is enough information to
solve the puzzle.

The facts that are needed are a) the radius of the sphere, and b) the diameter
of the hole -- at this point, the problem becomes one that we've all seen in
integral calculus.  All we know, however, is the length of the hole, not 
the diameter.

By Assumption 1, however, that information is sufficient.  In other words, the
diameter of the hole is irrelevant!  In that case, let d -> 0, the radius of
the sphere goes to 1/2 cm, and the volume of the ring goes to the volume
of the sphere less zero, or 4/3pi*(r^3) or pi/6 cm^3.

					q.e.d.

Anyone who feels mathematical might want to prove that this is the solution.
I.e. prove assumption 1.  I've done so, but don't want to deprive you of the
fun of so doing.
							Patrick Juola
							Hopkins Math
							...jhunix!ins_apmj