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ticbol
Posts:
116
Registered:
1/25/05


Re: largest cube inside sphere
Posted:
Feb 11, 2006 6:27 AM


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 So, 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 ] ***



