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# A sphere is inscribed in a cube with an edge of 10. What is

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Director
Joined: 10 Feb 2006
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A sphere is inscribed in a cube with an edge of 10. What is [#permalink]  28 Sep 2006, 18:17
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?

10( â€“ 1)

5

10( â€“ 1)

5( â€“ 1)

5( â€“ 1)
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Intern
Joined: 17 Apr 2006
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Re: Sphere - challenging [#permalink]  28 Sep 2006, 18:35
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?

10( â€“ 1)

5

10( â€“ 1)

5( â€“ 1)

5( â€“ 1)

I think the answer choices are incorrect. Nevertheless the solution is as follows.

Its easier to visualize this in 2 dimensions first. The shortest distance equals half the length of the diagonal minus the radius

Diameter of sphere = length of one of its edge = 10

Length of solid diagonal in the cube = sqrt(10^2 + 10^2 + 10^2)
= 10sqrt(3)
Half its length = 5sqrt(3) - 5
= 5 (sqrt(3) - 1)
VP
Joined: 25 Jun 2006
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What the hell with the answer choices?
Senior Manager
Joined: 28 Aug 2006
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Wrong options......

Go here:
http://www.gmatclub.com/phpbb/viewtopic.php?t=35891
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