Find the diagonal of the Cube

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

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++

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// CPP program to find length 
// of the diagonal of the cube 
#include <bits/stdc++.h>
using namespace std;
  
// Function to find length 
// of diagonal of cube
float diagonal_length(float a)
{
    float L;
  
    // Formula to Find length 
    // of diagonal of cube
    L = a * sqrt(3);
  
    return L;
}
  
// Driver code
int main()
{
  
    float a = 5;
  
    // Function call
    cout << diagonal_length(a);
  
    return 0;
}

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Java

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// Java program to find length 
// of the diagonal of the cube
class 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

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Python3

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

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C#

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// C# program to find length 
// of the diagonal of the cube 
using System;
class 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()
{
    float a = 5;
  
    // Function call
    Console.Write(diagonal_length(a));
}
}
  
// This code is contributed by Nidhi

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PHP

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<?php
// PHP program to find length 
// of the diagonal of the cube 
  
// Function to find length 
// of diagonal of cube
function diagonal_length($a)
{
    $L;
  
    // Formula to Find length 
    // of diagonal of cube
    $L = $a * sqrt(3);
  
    return $L;
}
  
// Driver code
$a = 5;
  
// Function call
echo diagonal_length($a);
  
// This code is contributed
// by Naman_Garg.
?>

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Output:

8.66025


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