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Topic: largest cube inside sphere
Replies: 6   Last Post: Feb 16, 2006 4:27 PM

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Posts: 116
Registered: 1/25/05
Re: largest cube inside sphere
Posted: Feb 11, 2006 6:27 AM
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G.E. Ivey wrote:
> > I have a what hopefully is a rather simple problem,
> > that has stumped two of my teachers and my boss.
> >
> > I have a a sphere of a given size 24" inside
> > diameter. I'm simply trying to mathematically find
> > out what is the largest cube that can fit inside a
> > sphere of a Given Diamter.
> > This is for a fabrication project and I have a
> > relatively true sphere, and I need to build a fitting
> > cubic box frame to go inside (1/8" tolerance). I've
> > tried using a descriptive geometry route and still
> > no luck.
> >
> > Any tips or pointers the most I got was taking an> angle off of the diagnol but that might be how to
> > solve for the largest square inside a circle (which
> > doesn't help)

Try this.
Draw a circle. Draw a diameter that is 45 degrees slanted from vertical
or from horizontal. Draw a square making that same diameter as a
diagonal of the square. Call a side of this square as "s".
By Pythagorean Theorem, in any of the two right triangles formed,
s^2 +s^2 = (diameter)^2
If the diameter = 24",
2s^2 = (24)^2
s^2 = (24*24)/2 = 288
s = sqrt(288) = 16.97 inches.
That is the side of the largest cube that you can get from a sphere of
diameter 24 inches.

If the diameter is not given, then the largest cube will have a side
that is
s = sqrt[(1/2)*(diameter)^2 ] -----------***

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