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 : 5.19615Input : 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 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 cube using 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 |
PHP
<?php// PHP program to find length // of the diagonal of the cube // Function to find length // of diagonal of cubefunction diagonal_length($a){ $L; // Formula to Find length // of diagonal of cube $L = $a * sqrt(3); return $L;}// Driver code$a = 5;// Function callecho 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 cubefunction 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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