# GMAT Math : Calculating the diagonal of a cube

## Example Questions

### Example Question #1 : Calculating The Diagonal Of A Cube

What is the length of the diagonal of a cube if its side length is   ?

Explanation:

The diagonal of a cube extends from one of its corners diagonally through the cube to the opposite corner, so it can be thought of as the hypotenuse of a right triangle formed by the height of the cube and the diagonal of its base. First we must find the diagonal of the base, which will be the same as the diagonal of any face of the cube, by applying the Pythagorean theorem:

Now that we know the length of the diagonal of any face on the cube, we can use the Pythagorean theorem again with this length and the height of the cube, whose hypotenuse is the length of the diagonal for the cube:

### Example Question #2 : Calculating The Diagonal Of A Cube

is a cube and face has an area of . What is the length of diagonal of the cube

Explanation:

To find the diagonal of a cube we can apply the formula , where  is the length of the diagonal and where  is the length of an edge of the cube.

Since we are given an area of a face of the cube, we can find the length of an edge simply by taking its square root.

Here the length of an edge is 3.

Thefore the final andwer is .

### Example Question #3 : Calculating The Diagonal Of A Cube

What is the length of the diagonal  of cube , knowing that face  has diagonal equal to ?

Explanation:

To find the length of the diagonal of the cube, we can apply the formula, however, we firstly need to find the length of an edge, by applying the formula for the diagonal of the square.

where  is the diagonal of face ABCD, and , the length of one of the side of this square.

The length of  must be , which is the length of the edges of the square.

Therefore we can now use the formula for the length of the diagonal of the cube:

, where  is the length of an edge.

Since , we get the final answer .

### Example Question #4 : Calculating The Diagonal Of A Cube

A given cube has an edge length of . What is the length of the diagonal of the cube?

Not enough information provided

Explanation:

The diagonal  of a cube with an edge length  can be defined by the equation . Given  in this instance, .

### Example Question #5 : Calculating The Diagonal Of A Cube

A given cube has an edge length of . What is the length of the diagonal of the cube?

Not enough information provided

Explanation:

The diagonal  of a cube with an edge length  can be defined by the equation . Given  in this instance, .

### Example Question #6 : Calculating The Diagonal Of A Cube

A given cube has an edge length of . What is the length of the diagonal of the cube?

None of the above

Explanation:

The diagonal  of a cube with an edge length  can be defined by the equation . Given  in this instance, .

### Example Question #7 : Calculating The Diagonal Of A Cube

If a cube has a side length of , what is the length of its diagonal?