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

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Senior Manager
Joined: 21 Jun 2006
Posts: 282

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

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30 Jun 2007, 18:52
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45% (01:23) correct 55% (01:23) wrong based on 132 sessions

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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) $$10(\sqrt{3}- 1)$$
(B) $$5$$
(C) $$10(\sqrt{2} - 1)$$
(D) $$5(\sqrt{3} - 1)$$
(E) $$5(\sqrt{2} - 1)$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-100798.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 May 2014, 03:36, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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30 Jun 2007, 22:19
sh.distance=[diagonal of cube - diameter of sphere]/2

which is [10*sqrt3 - 10]/2 =5*sqrt3-5

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Joined: 14 May 2014
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Re: Sphere is inscribed in a cube of side length 10 cms. What is [#permalink]

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21 May 2014, 09:40
Diagonal of the cube = 10*sqrt (3)
Diameter of Sphere = 10 cm

Diagonal of the cube will cross the center of sphere and it is perpendicular on the surface of sphere.

Smallest distance is the perpendicular distance from a surface

If we subtract diameter of sphere from diagonal of cube , we will get the part of diagonal which is out of the sphere.

since it contains two sides

minimum distance = (10 sqrt(3) - 10)/2 = 5*sqrt(3) - 5
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Re: Sphere is inscribed in a cube of side length 10 cms. What is [#permalink]

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22 May 2014, 03:37
Expert's post
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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) $$10(\sqrt{3}- 1)$$
(B) $$5$$
(C) $$10(\sqrt{2} - 1)$$
(D) $$5(\sqrt{3} - 1)$$
(E) $$5(\sqrt{2} - 1)$$

Shortest distance=(diagonal of cube-diameter of sphere)/2= $$\frac{10*\sqrt{3}-10}{2}=5(\sqrt{3}-1)$$

Answer: D.

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Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-100798.html
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Re: Sphere is inscribed in a cube of side length 10 cms. What is   [#permalink] 22 May 2014, 03:37
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# Sphere is inscribed in a cube of side length 10 cms. What is

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