Find the diagonal of the Cube

• Last Updated : 17 Mar, 2021

Given a side of the cube a. The task is to find the length of the diagonal of the cube. Examples:

Input : a = 3
Output : 5.19615
Input : a = 6
Output : 10.3923

Formula :

Length of diagonal of the cube = sqrt(3) * side

Proof :

Use Pythagorean Theorem,
In triangle CED,
CE2 = CD2 + DE2
l2 = a2 + a2 ———>(1)
In triangle CFE,
CF2 = CE2 + EF2
L2 = l2 + a2
use l2 value from equation(1),
L2 = a2 + a2 + a2
= 3*a2
L = sqrt(3) * a

C++

 // CPP program to find length// of the diagonal of the cube#include using namespace std; // Function to find length// of diagonal of cubefloat diagonal_length(float a){    float L;     // Formula to Find length    // of diagonal of cube    L = a * sqrt(3);     return L;} // Driver codeint main(){     float a = 5;     // Function call    cout << diagonal_length(a);     return 0;}

Java

 // Java program to find length// of the diagonal of the cubeclass GFG{         // Function to find length    // of diagonal of cube    static float diagonal_length(float a)    {        float L;                 // Formula to Find length        // of diagonal of cube        L = a * (float)Math.sqrt(3);                 return L;    }         // Driver Code    public static void main (String[] args)    {        float a = 5;                 // Function call        System.out.println(diagonal_length(a));    }} // This code is contributed by// sanjeev2552

Python3

 # Python3 program to find length# of the diagonal of the cubefrom math import sqrt # Function to find length# of diagonal of cubedef diagonal_length(a):    L = 0     # Formula to Find length    # of diagonal of cube    L = a * sqrt(3)     return L # Driver codea = 5 # Function callprint(diagonal_length(a)) # This code is contributed by Mohit Kumar

C#

 // C# program to find length// of the diagonal of the cubeusing System;class GFG{// Function to find length// of diagonal of cubestatic float diagonal_length(float a){    float L;     // Formula to Find length    // of diagonal of cube    L = a * (float)Math.Sqrt(3);     return L;} // Driver codepublic static void Main(){    float a = 5;     // Function call    Console.Write(diagonal_length(a));}} // This code is contributed by Nidhi



Javascript


Output:
8.66025

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