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sphere is inscribed in a cube

by sanju09 » Fri Mar 04, 2011 1:53 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?
(A) 10 (√3 - 1)
(B) 5
(C) 10 (√2 - 1)
(D) 5 (√3 - 1)
(E) 5 (√2 - 1)
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by Anurag@Gurome » Fri Mar 04, 2011 2:20 am
sanju09 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?
(A) 10 (√3 - 1)
(B) 5
(C) 10 (√2 - 1)
(D) 5 (√3 - 1)
(E) 5 (√2 - 1)
The shortest distance will be equal to the difference of the distance of the middle point of the cube from one of the vertices and the radius of the sphere.

The distance of the middle point of the cube from one of the vertices = (Length of the diagonal of the cube)/2 = (√3)*(Length of an edge of the cube)/2 = 5√3

Radius of the circle = (Length of an edge of the cube)/2 = 5

Hence, the required shortest distance = (5√3 - 5) = 5(√3 - 1)

The correct answer is D.
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