Find the diagonal of the Cube

Namachila 2 minutes ago

0 0 2 minutes read

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++

// 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;
}

Java

// 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

Python3

# 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

C#

// 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

PHP

<?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.
?>

Javascript

<script>
// javascript program to find length 
// of the diagonal of the cube 
 
// Function to find length 
// of diagonal of cube
function diagonal_length( a)
{
    let L;
 
    // Formula to Find length 
    // of diagonal of cube
    L = a * Math.sqrt(3);
 
    return L;
}
 
// Driver code
    let a = 5;
 
    // Function call
    document.write(diagonal_length(a).toFixed(5));
     
// This code is contributed by gauravrajput1 
</script>

Output:

8.66025

Time Complexity: O(1), as using sqrt(3) will take constant operations.
Auxiliary Space: O(1)

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