If the volume of a cube is 1 cubic centimeter, then the distance from

D
Side of the cube =1 cm
Distance between the opposite vertices = sqrt(3)

Hence the distance between the vertex to the center of the cube =sqrt(3)/2


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From one vertex of a cube to the center is half the length of the "space" diagonal that runs from one vertex, through the center, to a vertex on the opposite side.

The length of the space diagonal, D, is found with a variation on the Pythagorean theorem:

\(L^2 + W^2+ H^2 = D^2\)

Find side length(s):
The cube's volume, in cubic centimeters, is
\(s^3 = 1\)
\(\sqrt[3]{s^3} = \sqrt[3]{1}\)
So \(s = 1\)
Length, width, and height = 1

Using space diagonal formula:
\(1^2 + 1^2 + 1^2 = D^2\)
\(3 = D^2\)
\(\sqrt{3} = \sqrt{D^2}\)
\(D = \sqrt{3}\)

We need half that distance:
\(\frac{\sqrt{3}}{2}\)

Answer D

P.S. Bunuel , I believe your signature, or something in your posts, is not following BBCode (?). There is a long string of code that is not formatted.
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Looks fine to me. Did you try reloading couple of times?
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Bunuel, just switched browsers. No idea what is wrong with the other, but this one works. Thanks!
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Cube:
Length of diagonal between two vertices on the same plane= side*√2

And,Length of diagonal between two vertices in the different plane= side*√3.
This longer diagnol also passes through center point of cube at midway.

So, for a cube with volume 1 cubic centimeter, Each side = 1 cm.

So, Long Diagonal= √3 cm and midpoint is √3/2 cm from each vertex.

Hence, Ans D

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We need to calculate half of the Diagnol length of the cube.

(Diagonal length )^2 = one side^2 + Diagnol of square^2.
= 1 + (\sqrt{2})^2.
= \sqrt{3}.

Half of Diagnol = \sqrt{3}/2.
Ans D

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