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# The length of each edge of a cube equals 6. What is the dis

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The length of each edge of a cube equals 6. What is the dis [#permalink]  26 Aug 2017, 02:22
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The length of each edge of a cube equals 6. What is the distance between the center of the cube to one of its vertices?

A. $$3 \sqrt{2}$$

B. $$6 \sqrt{2}$$

C. $$3 \sqrt{3}$$

D. $$4 \sqrt{3}$$

E. $$6 \sqrt{3}$$
[Reveal] Spoiler: OA

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Re: The length of each edge of a cube equals 6. What is the dis [#permalink]  15 Sep 2017, 00:43
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There is a shortcut for this The diagonal of Cube can be founded by the formula: Sqrt(Asqr+Bsqr+Csqr).Here A=B=C=6.
So diagonal is SQRT(36+36+36)=6sqrt3
from centre, Divide by 2.ie 3sqrt3.
Feel free to ask any questions.
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Re: The length of each edge of a cube equals 6. What is the dis [#permalink]  18 Sep 2017, 01:04
Pushkar96 wrote:
There is a shortcut for this The diagonal of Cube can be founded by the formula: Sqrt(Asqr+Bsqr+Csqr).Here A=B=C=6.
So diagonal is SQRT(36+36+36)=6sqrt3
from centre, Divide by 2.ie 3sqrt3.
Feel free to ask any questions.

It is even faster to remember that the diagonal of a cube is $$l*sqrt(3)$$. Three dimensions, $$sqrt(3)$$; while the square, two dimensions $$sqrt(2)$$
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Re: The length of each edge of a cube equals 6. What is the dis [#permalink]  21 May 2018, 10:30
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Carcass wrote:

The length of each edge of a cube equals 6. What is the distance between the center of the cube to one of its vertices?

A. $$3 \sqrt{2}$$

B. $$6 \sqrt{2}$$

C. $$3 \sqrt{3}$$

D. $$4 \sqrt{3}$$

E. $$6 \sqrt{3}$$

The distance between the center of the cube to one of its vertices is half the length of the space diagonal of the cube. A space diagonal of a cube is the diagonal from one vertex of the cube to another vertex where the two vertices are not on the same face of the cube. Furthermore, if each edge of a cube has length s, then the space diagonal has a length of s√3.

We see that the space diagonal of the cube is 6√3, so half of that is 3√3.

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Re: The length of each edge of a cube equals 6. What is the dis   [#permalink] 21 May 2018, 10:30
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