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

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
If the volume of a cube is 1 cubic centimeter, then the distance from  [#permalink]

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30 Nov 2017, 22:55
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71% (01:12) correct 29% (01:06) wrong based on 44 sessions

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If the volume of a cube is 1 cubic centimeter, then the distance from any vertex to the center point inside the cube is

(A) 1/2 cm
(B) √2/2 cm
(C) √2 cm
(D) √3/2 cm
(E) √3 cm

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Re: If the volume of a cube is 1 cubic centimeter, then the distance from  [#permalink]

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30 Nov 2017, 23:30
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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Senior SC Moderator
Joined: 22 May 2016
Posts: 2117
If the volume of a cube is 1 cubic centimeter, then the distance from  [#permalink]

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Updated on: 01 Dec 2017, 07:53
1
Bunuel wrote:
If the volume of a cube is 1 cubic centimeter, then the distance from any vertex to the center point inside the cube is

(A) 1/2 cm
(B) √2/2 cm
(C) √2 cm
(D) √3/2 cm
(E) √3 cm

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:
$$\frac{\sqrt{3}}{2}$$

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.

Originally posted by generis on 01 Dec 2017, 07:47.
Last edited by generis on 01 Dec 2017, 07:53, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50730
Re: If the volume of a cube is 1 cubic centimeter, then the distance from  [#permalink]

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01 Dec 2017, 07:53
1
genxer123 wrote:
Bunuel wrote:
If the volume of a cube is 1 cubic centimeter, then the distance from any vertex to the center point inside the cube is

(A) 1/2 cm
(B) √2/2 cm
(C) √2 cm
(D) √3/2 cm
(E) √3 cm

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:

$$L^2 + W^2+ H^2 = D^2$$

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:
$$\frac{\sqrt{3}}{2}$$

P.S. Bunuel , I believe your signature is not following BBCode (?). There is a long string of code that is not formatted.

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Senior SC Moderator
Joined: 22 May 2016
Posts: 2117
If the volume of a cube is 1 cubic centimeter, then the distance from  [#permalink]

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01 Dec 2017, 12:49
Bunuel wrote:
genxer123 wrote:

P.S. Bunuel , I believe your signature is not following BBCode (?). There is a long string of code that is not formatted.

Bunuel, just switched browsers. No idea what is wrong with the other, but this one works. Thanks!
Manager
Joined: 01 Feb 2017
Posts: 171
Re: If the volume of a cube is 1 cubic centimeter, then the distance from  [#permalink]

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02 Dec 2017, 07:28
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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Re: If the volume of a cube is 1 cubic centimeter, then the distance from &nbs [#permalink] 02 Dec 2017, 07:28
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