The length of each edge of a cube equals 6. What is the distance betwe

Question

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}

houston1980 · Answer

The diagonal of a cube is  L \sqrt{3}  where "L" is the length of each side of the cube.

The diagonal of the above cube is therefore  6 \sqrt{3}

The distance between the center of the cube to one of its vertices is half of the diagonal = 0.5*  6 \sqrt{3}  =  3 \sqrt{3}

Hence  option  C =  3 \sqrt{3}      is the answer.

EgmatQuantExpert · Answer

Solution

Given:  
• The length of each edge of the cube considered is 6

To find:  
• The distance between the center of the cube to any of the vertices

Approach and Working:   
When we are considering the distance between the center of the cube and any of the vertices, we need to consider the shortest possible distance only, which is along the diagonal of the cube
• Length of a diagonal of the cube =  \sqrt{3}  * length of the side =  \sqrt{3} * 6 = 6\sqrt{3} 
• As we are measuring the distance from the center, it will be half the length of diagonal
 o Therefore, distance between the center of the cube to any of the vertices =  \frac{1}{2} * 6\sqrt{3} = 3\sqrt{3}

Hence, the correct answer is option C.

Answer: C

JeffTargetTestPrep · Answer

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.

Answer: C

akadiyan · Answer

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?

Known Information:
The length of each edge of cube equals 6.

We know that distance between 2 edges of a cube is equal to diagonal. So we have the diagonal as 63.

Question:
What is the distance between the center of the cube to one of its vertices?

Since question ask distance between center of cube to one of its vertices, we need to divide the value of diagonal by half.

6 \sqrt{3}  / 2 = 3 \sqrt{3}

Ans:   C

SSM700plus · Answer

.

Solution:-

the distance between the center of the cube to one of its vertices = half the length of diagonal of cube.

diagonal of one side of cube is nothing but diagonal of square. Diagonal of square =  \sqrt{6^2 + 6^2}  =  6\sqrt{2}

Diagonal of Cube = \sqrt{(6 2})^2 + 6^2  =  \sqrt{72 + 36}  =  \sqrt{108}  =  6\sqrt{3}

the distance between the center of the cube to one of its vertices =  \frac{6}{2} * \sqrt{3}  =  3\sqrt{3}

Ans - C

The length of each edge of a cube equals 6. What is the distance betwe

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The length of each edge of a cube equals 6. What is the distance betwe

Prep Toolkit

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