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The length of one edge of a cube equals \(4.\) What is the distance between the center of the cube and one of its vertic

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by Gmat_mission » Thu May 21, 2020 1:39 am

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The length of one edge of a cube equals \(4.\) What is the distance between the center of the cube and one of its vertices?

A) \(4\sqrt2\)
B) \(3\sqrt2\)
C) \(2\sqrt3\)
D) \(3\sqrt3\)
E) \(5\sqrt3\)

[spoiler]OA=C[/spoiler]

Source: Manhattan GMAT
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Source: — Problem Solving |

Gmat_mission wrote:
Thu May 21, 2020 1:39 am
The length of one edge of a cube equals \(4.\) What is the distance between the center of the cube and one of its vertices?

A) \(4\sqrt2\)
B) \(3\sqrt2\)
C) \(2\sqrt3\)
D) \(3\sqrt3\)
E) \(5\sqrt3\)

[spoiler]OA=C[/spoiler]

Solution:

The distance between the center of the cube and one of its vertices is ½ the length of the space diagonal of the cube. Since the edge of the cube has a length of 4, the length of the space diagonal is 4√3 and thus the distance sought is 2√3.

Answer: C

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