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

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Re: A sphere is inscribed in a cube with an edge of 10. What is  [#permalink]

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12 Nov 2016, 00:33
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enigma123 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) $$10(\sqrt{3}- 1)$$
(B) $$5$$
(C) $$10(\sqrt{2} - 1)$$
(D) $$5(\sqrt{3} - 1)$$
(E) $$5(\sqrt{2} - 1)$$

Answer: Option D (Just replace edge length as 10 instead of 20)

Check solution as attached
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Re: A sphere is inscribed in a cube with an edge of 10. What is  [#permalink]

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19 Dec 2018, 21:48
Hi, so I originally solved this as

5(2‾√−1) is this because I took this problem to be a circle inside a square vs a sphere inside a cube?

Is the formula I need to memorize 10(3‾√? I can't seem to follow the direction/image provided below.

What is the diagonal of the face of the cube and then the diagonal through the center? PS - I can't seem to do the square root function in my copy and paste!

The diagonal of a cube of side x is x. This can be found by applying the Pythagorean Theorem twice (first to find the diagonal of a face of the cube, x, and then to find the diagonal through the center, x).
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Re: A sphere is inscribed in a cube with an edge of 10. What is  [#permalink]

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14 Sep 2019, 12:19
enigma123 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) $$10(\sqrt{3}- 1)$$
(B) $$5$$
(C) $$10(\sqrt{2} - 1)$$
(D) $$5(\sqrt{3} - 1)$$
(E) $$5(\sqrt{2} - 1)$$

diagonal of the cube ; 10√3 and diameter of circle ; 10 radius=5
half of (Diagonal minus Diameter) is a gap between the vertex of a cube and the surface of the sphere, which will be the shortest distance 10√3-10/2 = $$5(\sqrt{3} - 1)$$
IMO D
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Re: A sphere is inscribed in a cube with an edge of 10. What is   [#permalink] 14 Sep 2019, 12:19

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