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by gmatnmein2010 » Mon Feb 08, 2010 5:35 am
3. 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?
(A 10( sqrt3- 1)
(B) 5
(C) 10( sqrt2 - 1)
(D) 5( sqrt3 - 1)
(E) 5( sqrt2 - 1)
kindly show me the steps for this
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by shashank.ism » Mon Feb 08, 2010 6:01 am
gmatnmein2010 wrote:3. 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?
(A 10( sqrt3- 1)
(B) 5
(C) 10( sqrt2 - 1)
(D) 5( sqrt3 - 1)
(E) 5( sqrt2 - 1)
kindly show me the steps for this
radius of sphere = 10/2 =5
distance from centre to vertices = 10(sqrt. 2)/2 = 5(sqrt. 2)

so shortest possible distance from one of the vertices of the cube to the surface of the sphere = [spoiler]5( sqrt2 - 1)
Ans is E[/spoiler]
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by thephoenix » Mon Feb 08, 2010 6:44 am
Shortest distance=(diagonal of cube-diameter of sphere)/2=(10*3^1/2-10)/2=5(3^1/2-1)
imo d
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by harsh.champ » Mon Feb 08, 2010 8:32 am
shashank.ism wrote:
gmatnmein2010 wrote:3. 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?
(A 10( sqrt3- 1)
(B) 5
(C) 10( sqrt2 - 1)
(D) 5( sqrt3 - 1)
(E) 5( sqrt2 - 1)
kindly show me the steps for this
radius of sphere = 10/2 =5
distance from centre to vertices = 10(sqrt. 2)/2 = 5(sqrt. 2)

so shortest possible distance from one of the vertices of the cube to the surface of the sphere = [spoiler]5( sqrt2 - 1)
Ans is E[/spoiler]
Hey shashank,
I think you made a mistake over there.Since we are considering a 3-D object(cube) not a 2-D object(square).
So,length of the diagonal will be 10sqrt(3),not 10sqrt(2).
Besides this,your method of solving is correct.
Hence,the answer will be D not E.

The E option was a trap by the question-setter.
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by ajith » Mon Feb 08, 2010 10:26 am
gmatnmein2010 wrote:3. 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?
(A 10( sqrt3- 1)
(B) 5
(C) 10( sqrt2 - 1)
(D) 5( sqrt3 - 1)
(E) 5( sqrt2 - 1)
kindly show me the steps for this
Square length of the diagonal of a cube joining totally opposite sides = (Sqrt(2)*a)^2 + a^2 = 3a^2
Length of the diagonal = a*sqrt(3)

Distance from the center of the sphere to the vertex = 1/2 full body diagonal = a/2 sqrt(3) = 5 sqrt(3)
Distance from the center of the sphere to the surface of the sphere = 1/2 *a = 5

Distance between vertex and surface of the sphere [spoiler]= 5 sqrt(3)-5 = 5( sqrt3 - 1) =(D)[/spoiler]
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