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Put a cork in it [original thread]


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19 replies to this topic

#11 plainglazed

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Posted 08 September 2009 - 11:53 AM

Spoiler for still

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#12 plasmid

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Posted 09 September 2009 - 04:43 AM

Spoiler for Hmmm

Spoiler for

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#13 cmgogo00

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Posted 10 September 2009 - 03:54 PM

the smallest hole is the triangle with an area of (2 x square root 3).. so the maximum volume must be smaller than 2x2x1.732(square root of 3)

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#14 Doctor Moshe

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Posted 10 September 2009 - 05:26 PM

I agree with various answers posted but to summarize
Spoiler for Both Answers

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#15 bonanova

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Posted 07 August 2012 - 03:00 AM

To revive this thread by means of a duplicate post was an oversight.
Nevertheless it contains the most discussion [the duplicate thread has none.]

One condition for the solid is that it be convex.
This rules out the zero-volume shapes.

The volume that has been put forward as the largest is convex,
but in fact it pertains to the convex solid with the smallest volume!

If it helps, the shape of the largest solid is the simplest, and has
a volume that's larger by almost 1 in3.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#16 austinm

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Posted 07 August 2012 - 03:30 PM

Spoiler for sketch of solid


Finding its volume was a fairly straightforward calculus problem. Letting the circular base lie in the x-y plane and the linear ridge lie along the y-axis:

Spoiler for volume, analytically


Of course, I had to go back to my CRC to look up some of the integrals, so I wouldn't be surprised if there were a small transcription error in there. Especially as my 3D-modeling program claims the volume is
Spoiler for volume, numerically


Anyone else find the volume of a solid that looks like this?

[edited to catch factor-of-2 error]

Edited by austinm, 07 August 2012 - 03:37 PM.

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#17 superprismatic

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Posted 08 August 2012 - 08:57 PM

Spoiler for what I found

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#18 plasmid

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Posted 09 August 2012 - 12:26 AM

Spoiler for what I found

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#19 superprismatic

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Posted 09 August 2012 - 01:52 AM

Spoiler for

I think you're correct. In that case, I think there is only one convex solid which works -- the minimum volume is the same as the maximum volume.
Spoiler for however...

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#20 EventHorizon

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Posted 10 August 2012 - 04:06 AM

...
The volume that has been put forward as the largest is convex,
but in fact it pertains to the convex solid with the smallest volume!

If it helps, the shape of the largest solid is the simplest, and has
a volume that's larger by almost 1 in3.


I've got a convex solid with a smaller volume than the one posted so far...
Spoiler for Minimum?


As of yet, I'm still at a loss for the solid with the maximum volume.
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