Diagonal Of A Cube Formula

Diagonal of a Cube Formula

A Cube’s diagonal line segment joins any two of its non-adjacent vertices. Due to the fact that it has 12 equally spaced edges and is one of the most prevalent forms in the environment, the Cube is one of the most significant geometric shapes. Some examples of Cubes are ice, sugar Cubes, Rubik’s Cubes, dice, and other everyday objects. A Cube has two different types of diagonals because it is a three-dimensional object.

A Cube is a solid three-dimensional object. The square solid with uniformly long edges is referred to as a Cube. In other words, each of its faces is a square, and its length, breadth, and height are all equal. The diagonal that runs through the middle of a Cube is its main diagonal; the diagonal that runs along one of its faces is not. Any Diagonal Of A Cube Formula can be calculated by multiplying one side’s length by the square root of three.

What is Diagonal of a Cube?

The length of the line segment that joins any two of the Cube’s non-adjacent vertices can be calculated using the Diagonal Of A Cube Formula. The Cube is a predominantly found shape in the environment due to its distinctive quality of possessing 12 equally spaced edges. Ice cubes, sugar Cubes, Rubik’s Cubes, dice, and other everyday objects are notable examples of the geometrical shape known as a Cube. A Cube is a three-dimensional object. Therefore, it has different kinds of diagonals.

The line that passes through the Cube’s center is considered to be its diagonal. The Cube’s face diagonal is simple to determine. However, it is not the major diagonal of a Cube. The length of a Cube’s sides, which are all equal, can be multiplied by the square root of 3 to discover the diagonal of a Cube. Students can quickly and easily remove the diagonal of a Cube using this simple calculation. 

A Cube is a particular type of cuboid in which all cuboid faces are of identical length. The cuboid has six rectangular faces that make up its faces. The cuboid eventually transforms into a Cube if the rectangles have the same lengths of sides.

Face Diagonal of a Cube

Six square-shaped faces make up a Cube. Two Diagonal Of A Cube Formula on each face connect the vertices that are not adjacent. Consequently, a Cube has 12 face diagonals.

Body Diagonal of a Cube

The Diagonal Of A Cube Formula joins its opposing vertices while traversing its body. As a result, a Cube has four body diagonals that go through it and join the opposite corners.

Diagonal of Cube Formula

The length of a Diagonal Of A Cube Formula can be calculated according to the specified parameters and requirements.

Length of Face Diagonal of a Cube

Determines a Diagonal Of A Cube Formula length is written as

Length of each face diagonal of Cube = √2a, where a = Length of each Cube side.

Length of Body Diagonal of a Cube

The following equation can be used to determine the length of a Cube’s space or body diagonal:

Length of each body Diagonal Of A Cube Formula = √3a, where a = Length of each side of a Cube.

Derivation of Diagonal of a Cube Formula

In the Diagonal Of A Cube Formula, the diagonal usually refers to the Cube’s body diagonal. The Pythagoras theorem can be used to derive this formula.

One can think of the Cube’s side as “a,” its face diagonal as “r,” and its body diagonal as “d.” Once the face diagonal and the body diagonal are connected, one can see that a right-angled triangle with the sides a, r, and d is created. In the resulting right-angled triangle, the body diagonal becomes the hypotenuse.

Examples Using Diagonal of a Cube Formula

  • Example 1: Calculate the length of the body diagonal of a Cube whose each side measures 5 units.

Solution:

Given, the length of each side of the Cube (a) = 5 units; body diagonal = ?

So, let us substitute the given values in the Diagonal Of A Cube Formula,

Length of body Diagonal Of A Cube Formula = √3a

= √3 × 5 = 8.66 units

Therefore, the length of the body diagonal of the given Cube = 8.66 units.

  • Example 2: Find the diagonal of the Cube with the given side 5 cm.

Solution:

Given: side x = 5 cm

Use the Diagonal Of A Cube Formula

Diagonal of Cube =

3x

Diagonal of Cube =

3∗5

It is known that the value of √3 is 1.734

Therefore, the diagonal of a Cube = 1.734 (5)

Diagonal of Cube = 8.67 cm

  • Example 3: The length of the body diagonal of a Cube is 8√3 units. Find the length of each side of the Cube.

Solution:

Given, body diagonal = 8√3 units; length of each side of the Cube (a) = ?

We know that the Diagonal Of A Cube Formula is expressed as,

Length of body diagonal of a Cube = √3a

So, one can substitute the given values in the formula to get the unknown value,

Length of body diagonal of a Cube = √3a

⇒ 8√3 = √3a

⇒ a = 8

Therefore, the length of each side of the given Cube = 8 units

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FAQs (Frequently Asked Questions)

A Cube has four body diagonals because it is a three-dimensional figure. The “space diagonal” or “solid diagonal” of a Cube are other names for a body diagonal. The Cube’s body diagonals join its opposing vertices while traversing its body. As a result, a Cube has four body diagonals that go through it and join the opposite corners.

The following is the Diagonal Of A Cube Formula to determine the length of a Cube’s body diagonal or main diagonal: The length of a Cube’s body diagonal is equal to Cube = √3a, where an is the length of each side.

The length of the line segment that connects any two non-adjacent Cube vertices can be calculated with the aid of the Diagonal Of A Cube Formula. A Cube features two different types of diagonals, face diagonals, and body diagonals because it is a three-dimensional (3D) shape. The Diagonal Of A Cube Formula that is produced on a Cube’s six faces is known as the face diagonal. Additionally, a Cube has 12 face diagonals because two diagonals can be created on each face. 

Students are all aware that a Cube has uniformly long edges. It is quite simple to subtract a diagonal’s length when one has to. All you need to do is ensure you know the proper side length. The Pythagoras theorem may be applied now that all the sides are the same length since a right-angled triangle is formed by the Cube’s two edges and a diagonal on the same face. When the Pythagoras theorem is applied correctly, and the edge lengths are known, this process can be completed quickly and easily.

The sides of a Cube are all the same length. It is also possible to determine that the diagonals’ angle is 90 degrees. Students can be certain to have the lengths of the sides with them in order to demonstrate this. When they do, they have the opportunity to determine the result of the Diagonal Of A Cube Formula as well. The Pythagoras Theorem makes it fairly simple to determine the actual lengths of a Cube’s diagonals.