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by gmatnmein2010 » Sat Feb 20, 2010 3:46 am
A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?


1)10( - 1)



2)5


3)10( - 1)



4)5( - 1)



5)5( - 1)
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by ajith » Sat Feb 20, 2010 4:02 am
gmatnmein2010 wrote:A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?


1)10( - 1)



2)5


3)10( - 1)



4)5( - 1)



5)5( - 1)
Question already discussed here https://www.beatthegmat.com/tough-gemoet ... t8764.html

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by harsh.champ » Sat Feb 20, 2010 4:09 am
gmatnmein2010 wrote:A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?


1)10( - 1)



2)5


3)10( - 1)



4)5( - 1)



5)5( - 1)
Length of diagonal of cube =10 x sqrt(3)
Radius of sphere = half length of the cube = 5
Half length of diagonal = 5 x sqrt(3)

Thus,the shortest possible distance will be (Half length of diagonal) - (Radius of sphere) = 5 [sqrt(3) -1]
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by harsh.champ » Sat Feb 20, 2010 4:11 am
gmatnmein2010 wrote:A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?


1)10( - 1)



2)5


3)10( - 1)



4)5( - 1)



5)5( - 1)
Hey gmatmein 2010,
I think you left the sqrt(3) in all the options choices .I guess maybe it was a small image which couldn't get copied.
In that case the answer would be D.
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by shashank.ism » Sat Feb 20, 2010 9:19 am
gmatnmein2010 wrote:A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?
1)10( - 1)
2)5
3)10( - 1)
4)5( - 1)
5)5( - 1)
Half length of diagonal of cube =5xsqrt(3)
Radius of sphere = 5
Thus,the shortest possible distance = 5[sqrt(3) -1]
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