Find the diagonal of the Cube Last Updated : 23 Sep, 2022 Comments Improve Suggest changes Like Article Like Report 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 <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) Comment More infoAdvertise with us Next Article Analysis of Algorithms N nidhiva Follow Improve Article Tags : Mathematical Geometric DSA Practice Tags : GeometricMathematical Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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