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# Sphere is inscribed in a cube of side length 10 cms. What is

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SVP
Joined: 29 Aug 2007
Posts: 2453
Sphere is inscribed in a cube of side length 10 cms. What is [#permalink]

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03 Aug 2008, 23:08
Sphere is inscribed in a cube of side length 10 cms. What is the shortest distance from any of the vertices of the cube to the sphere surface?

a. 5
b. 10
c. 5-sqrt(3)
d. 10-sqrt(3)
e. 10-s*sqrt(3)

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Director
Joined: 27 May 2008
Posts: 539

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03 Aug 2008, 23:23
GMAT TIGER wrote:
Sphere is inscribed in a cube of side length 10 cms. What is the shortest distance from any of the vertices of the cube to the sphere surface?

a. 5
b. 10
c. 5-sqrt(3)
d. 10-sqrt(3)
e. 10-s*sqrt(3)

diagonal of the cube = 10sqrt(3)
half of it = 5sqrt(3)
radius of the sphere = 5
shortest distance = 5sqrt(3) - 5
... this is not an option. ... could you check the question...
Manager
Joined: 23 Apr 2008
Posts: 83

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03 Aug 2008, 23:44
I AGREE..

10SQRT3 - 10/2
WHICH GIVES 5 SQRT3 - 5
Senior Manager
Joined: 07 Jan 2008
Posts: 384

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04 Aug 2008, 00:58
Agree,
$$5*sqrt{3} - 5$$
VP
Joined: 17 Jun 2008
Posts: 1325

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05 Aug 2008, 19:28
GMAT TIGER wrote:
Sphere is inscribed in a cube of side length 10 cms. What is the shortest distance from any of the vertices of the cube to the sphere surface?

a. 5
b. 10
c. 5-sqrt(3)
d. 10-sqrt(3)
e. 10-s*sqrt(3)

radius of the largest sphere in a cube of length 5 is 5
dist between vertex of cube to center of sphere is 5(3^1/2)
hence shortest dis between vertex of cube to surface = 5*sqrt(3)-5

OA =???

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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cheers
Its Now Or Never

Re: Shortest Length   [#permalink] 05 Aug 2008, 19:28
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# Sphere is inscribed in a cube of side length 10 cms. What is

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