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March 3rd, 2019, 02:55 AM  #1 
Newbie Joined: Mar 2019 From: Australia Posts: 6 Thanks: 0  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 
March 3rd, 2019, 02:58 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond 
What progress have you made?

March 3rd, 2019, 03:04 AM  #3 
Newbie Joined: Mar 2019 From: Australia Posts: 6 Thanks: 0  
March 3rd, 2019, 03:04 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond 
Well, post your work and we'll take it from there. 
March 3rd, 2019, 03:13 AM  #5 
Newbie Joined: Mar 2019 From: Australia Posts: 6 Thanks: 0 
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

March 3rd, 2019, 03:17 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond 
Can you type out your calculations and describe how each step relates to the cube/sphere problem?

March 3rd, 2019, 03:26 AM  #7  
Newbie Joined: Mar 2019 From: Australia Posts: 6 Thanks: 0  Quote:
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.  
March 3rd, 2019, 03:54 AM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond 
I have obtained s = D/sqrt(3) as well. It's possible that the given answer is incorrect.

March 3rd, 2019, 03:59 AM  #9  
Newbie Joined: Mar 2019 From: Australia Posts: 6 Thanks: 0  Quote:
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.  
March 3rd, 2019, 04:21 AM  #10 
Global Moderator Joined: Dec 2006 Posts: 20,629 Thanks: 2077 
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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