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March 3rd, 2019, 02:55 AM   #1
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Cube inside sphere

The largest cube that can fit into a sphere must have eight vertices touching the surface of the sphere. Express the side length, s, of the cube in terms of the diameter, D, of the sphere.
Posted this in the elementary forum, but realised there was an algebra forum, anyway quick responses appreciated
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March 3rd, 2019, 02:58 AM   #2
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What progress have you made?
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March 3rd, 2019, 03:04 AM   #3
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What progress have you made?
Well I know for a fact that the answer (at least said in the book) is s=root 3*D/3...
As for my working out, I've used Pythagoras theorem to try to find out my answer by dissecting the cube but none of my solutions match the answer.
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March 3rd, 2019, 03:04 AM   #4
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Well, post your work and we'll take it from there.
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March 3rd, 2019, 03:13 AM   #5
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Sorry I don't really have a camera and this problem is more visual so I don't really know how to "post" my work. Sorry for the inconvenience
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March 3rd, 2019, 03:17 AM   #6
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Can you type out your calculations and describe how each step relates to the cube/sphere problem?
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March 3rd, 2019, 03:26 AM   #7
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Can you type out your calculations and describe how each step relates to the cube/sphere problem?
Well I've drawn and labelled out my diagram, and my calculations are purely based on the diagram. I've got to go to sleep soon but if you don't mind here's a link to a similar problem https://www.quora.com/What-is-the-la...-of-diameter-2
The only difference is that there are no variables just the term 's' and 'D' and I'm not trying to find the volume, only the side length. My working out is quite similar, to the one in the link, but my answer doesn't equal the one that is given in the textbook. (My answer by the way is s=D/root 3)

Last edited by chickensoup; March 3rd, 2019 at 03:28 AM.
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March 3rd, 2019, 03:54 AM   #8
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I have obtained s = D/sqrt(3) as well. It's possible that the given answer is incorrect.
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March 3rd, 2019, 03:59 AM   #9
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I have obtained s = D/sqrt(3) as well. It's possible that the given answer is incorrect.
Quite possible. Anyway, thank you for replying so quickly, I was quite confused by this question, but now, looking back at it, I feel a little better. I'm really stressed, because I have a test tomorrow (Surds) and these are the type of questions coming up.
Thanks again.

Oh wait... lol - if you rationalise that, it turns into D sqrt3/3.

Last edited by skipjack; March 3rd, 2019 at 04:24 AM.
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March 3rd, 2019, 04:21 AM   #10
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If the cube's side length is s, its longest diagonal has length √(3s²) = √3s = D (by symmetry), where D is the sphere's diameter, so s = D/√3 = √3D/3.
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