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<DIV><FONT face=Arial size=2>I just did the calcs on a 12" diam. sphere to test
the theory. I just learned that you are absolutely correct, the volume is
constant because, too keep the hole length at 6" you have a larger diameter hole
the larger the diameter of the sphere.</FONT></DIV>
<DIV><FONT face=Arial size=2>Do I really have to type all of the
calcs?:-(</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Ken</FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=atwoodm@paragon-inc.com href="mailto:atwoodm@paragon-inc.com">Atwood,
Mark</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=discussion@nsrca.org
href="mailto:discussion@nsrca.org">discussion@nsrca.org</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, August 15, 2005 4:01
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> RE: PUZZLE!</DIV>
<DIV><BR></DIV>
<DIV class=Section1>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">DING DING DING…we
have a winner. Sort of… The number is right…meaning
that you’re taking the size of the sphere as the diameter of the cylinder
approaches zero. <o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">All your missing is
the key assumption…that the volume of the remaining material remains constant
regardless of the size of the Sphere…which is
true.<o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Now…for the big
bonus…do the proof!!!! (FYI, the proof is a
pain)<o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<DIV>
<DIV class=MsoNormal style="TEXT-ALIGN: center" align=center><FONT
face="Times New Roman" size=3><SPAN style="FONT-SIZE: 12pt">
<HR tabIndex=-1 align=center width="100%" SIZE=2>
</SPAN></FONT></DIV>
<P class=MsoNormal><B><FONT face=Tahoma size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Tahoma">From:</SPAN></FONT></B><FONT
face=Tahoma size=2><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Tahoma">
discussion-request@nsrca.org [mailto:discussion-request@nsrca.org] <B><SPAN
style="FONT-WEIGHT: bold">On Behalf Of </SPAN></B>Ken Thompson<BR><B><SPAN
style="FONT-WEIGHT: bold">Sent:</SPAN></B> Monday, August 15, 2005 4:01
PM<BR><B><SPAN style="FONT-WEIGHT: bold">To:</SPAN></B> <st1:PersonName
w:st="on">discussion@nsrca.org</st1:PersonName><BR><B><SPAN
style="FONT-WEIGHT: bold">Subject:</SPAN></B> Re:
PUZZLE!</SPAN></FONT><o:p></o:p></P></DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"><o:p> </o:p></SPAN></FONT></P>
<DIV>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">This is just a wild guess, I'm not
real good at these.</SPAN></FONT><o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">If the hole is of a very
small diameter that would make the sphere 6 inches in diameter.
</SPAN></FONT><o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">If the sphere is 6" in diameter
than the resulting volume would be...4/3 x pi x r cubed or
113.09733552924001</SPAN></FONT><o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">That's the best I can do on short
notice, with my minimal remaining brain
cells.</SPAN></FONT><o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Ken</SPAN></FONT><o:p></o:p></P></DIV>
<BLOCKQUOTE
style="BORDER-RIGHT: medium none; PADDING-RIGHT: 0in; BORDER-TOP: medium none; PADDING-LEFT: 4pt; PADDING-BOTTOM: 0in; MARGIN: 5pt 0in 5pt 3.75pt; BORDER-LEFT: black 1.5pt solid; PADDING-TOP: 0in; BORDER-BOTTOM: medium none">
<DIV>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">----- Original Message -----
<o:p></o:p></SPAN></FONT></P></DIV>
<DIV style="font-color: black">
<P class=MsoNormal style="BACKGROUND: #e4e4e4"><B><FONT face=Arial
size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Arial">From:</SPAN></FONT></B><FONT
face=Arial size=2><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <A
title=atwoodm@paragon-inc.com href="mailto:atwoodm@paragon-inc.com">Atwood,
Mark</A> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><B><FONT face=Arial size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Arial">To:</SPAN></FONT></B><FONT
face=Arial size=2><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <A
title=discussion@nsrca.org
href="mailto:discussion@nsrca.org">discussion@nsrca.org</A>
<o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><B><FONT face=Arial size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Arial">Sent:</SPAN></FONT></B><FONT
face=Arial size=2><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> Monday,
August 15, 2005 3:12 PM<o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><B><FONT face=Arial size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Arial">Subject:</SPAN></FONT></B><FONT
face=Arial size=2><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">
PUZZLE!<o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"><o:p> </o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Ok…this is by no
means Airplane related, but it seems to me that with all the engineers that
solicit this list-serve, we could have some fun with a few puzzles… So
since it’s slow (While we wait for the worlds to start next week) I thought
I’d post a fun one.<o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Imagine a Sphere
that has a cylindrical hole bored through the center, the diameter of which
results in the remaining hole being 6 inches long. What is the volume
of the remaining material in the sphere??<o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">And yes, you have
enough information, and yes, I’m looking for a numerical, absolute
answer!!<o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">-<st1:PersonName
w:st="on">Mark</st1:PersonName><o:p></o:p></SPAN></FONT></P></DIV></BLOCKQUOTE></DIV></BLOCKQUOTE></BODY></HTML>