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<DIV><FONT face=Arial size=2>I suppose I could show the equations for the top
and bottom caps, the sphere volume, the cylinder volume and then show the
remaining volume but that is way too much typing. Let's suffice to say
that it with a cylinder length of 6" the remaining volume will always be, in
the rounded version....36 x pi or 113.04, not the 113.09 that I
originally wrote.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>How'd I do?</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Ken</FONT></DIV>
<DIV><FONT face=Arial size=2></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>