Question

how many diagonal will be there in a cuboid​

Answer 1

four

There are four space diagonals, i.e. diagonals not contained in any face, illustrated in the diagram, below. In addition, in case this is a trick question, each face has two diagonals, for a total of 12 face diagonals (not shown). The faces of a big cube are painted. Then the cube is cut into 125 unit cubes.

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Answer 2

There are 16 Diagonals in a cuboid

Given:

• Cuboid

To Find:

• Number of Diagonals

Solution:

A cuboid has 8 Vertex , 6 faces and 12 Edges

Each vertex is connected to 3 other vertex.

Hence From a vertex  , (8 - 3 - 1) = 4 Diagonals can  be drawn  

(3 is subtracted as vertex is connected to 3 vertex and 1 is subtracted for vertex it self  , for remaining out of 8 it will form a diagonal)

Hence 8 x 4 = 32 Diagonals

But this process count each  Diagonal twice  like from Vertex 1 to vertex 3 as well as Vertex 3 to  Vertex 1 which are actually same.

Hence Number of Diagonals = 32/2 = 16

Another Method:

Each Face is a rectangle hence has 2 Diagonals

6 Faces will have 6 x 2 = 12 Diagonals

There will be 4 Diagonals between farthest Vertex

4  pairs of farthest vertex will create 4 Diagonals

12 + 4 = 16 Diagonals

Hence , There are 16 Diagonals in a cuboid