Given the length of edges of an irregular tetrahedron. The task is to determine the volume of that tetrahedron. Let the Edge length of pyramids be u, U, v, V, w, W.
Examples:
Input: u = 1000, v = 1000, w = 1000, U = 3, V = 4, W = 5 Output: 1999.9947 Input: u = 2000, v = 2000, w = 2000, U = 3, V = 4, W = 5 Output: 3999.9858
Formula to calculate the Volume of an irregular Tetrahedron in terms of its edge lengths is:
A =
Volume = sqrt(A/288) =
sqrt(4*u*u*v*v*w*w – u*u*(v*v + w*w – U*U)^2 – v*v(w*w + u*u – V*V)^2 – w*w(u*u + v*v – W*W)^2 + (u*u + v*v – W*W) * (w*w + u*u – V*V) * (v*v + w*w – U*U)) / 12
Below is the implementation of the above approach:
C++
// C++ implementation of above approach#include <bits/stdc++.h>using namespace std;#define db double// Function to find the volumevoid findVolume(db u, db v, db w, db U, db V, db W, db b){ // Steps to calculate volume of a // Tetrahedron using formula db uPow = pow(u, 2); db vPow = pow(v, 2); db wPow = pow(w, 2); db UPow = pow(U, 2); db VPow = pow(V, 2); db WPow = pow(W, 2); db a = 4 * (uPow * vPow * wPow) - uPow * pow((vPow + wPow - UPow), 2) - vPow * pow((wPow + uPow - VPow), 2) - wPow * pow((uPow + vPow - WPow), 2) + (vPow + wPow - UPow) * (wPow + uPow - VPow) * (uPow + vPow - WPow); db vol = sqrt(a); vol /= b; cout << fixed << setprecision(4) << vol;}// Driver codeint main(){ // edge lengths db u = 1000, v = 1000, w = 1000; db U = 3, V = 4, W = 5; db b = 12; findVolume(u, v, w, U, V, W, b); return 0;} |
Java
// Java implementation of above approachimport java.util.*;import java.lang.*;import java.io.*;class GFG{// Function to find the volumestatic void findVolume(double u, double v, double w, double U, double V, double W, double b){ // Steps to calculate volume of a // Tetrahedron using formula double uPow = Math.pow(u, 2); double vPow = Math.pow(v, 2); double wPow = Math.pow(w, 2); double UPow = Math.pow(U, 2); double VPow = Math.pow(V, 2); double WPow = Math.pow(W, 2); double a = 4 * (uPow * vPow * wPow) - uPow * Math.pow((vPow + wPow - UPow), 2) - vPow * Math.pow((wPow + uPow - VPow), 2) - wPow * Math.pow((uPow + vPow - WPow), 2) + (vPow + wPow - UPow) * (wPow + uPow - VPow) * (uPow + vPow - WPow); double vol = Math.sqrt(a); vol /= b; System.out.printf("%.4f",vol);}// Driver codepublic static void main(String args[]){ // edge lengths double u = 1000, v = 1000, w = 1000; double U = 3, V = 4, W = 5; double b = 12; findVolume(u, v, w, U, V, W, b);} } |
Python3
# Python 3 implementation of above approach # from math lib import everythingfrom math import *# Function to find the volume def findVolume(u, v, w, U, V, W, b) : # Steps to calculate volume of a # Tetrahedron using formula uPow = pow(u, 2) vPow = pow(v, 2) wPow = pow(w, 2) UPow = pow(U, 2) VPow = pow(V, 2) WPow = pow(W, 2) a = (4 * (uPow * vPow * wPow) - uPow * pow((vPow + wPow - UPow), 2) - vPow * pow((wPow + uPow - VPow), 2) - wPow * pow((uPow + vPow - WPow), 2) + (vPow + wPow - UPow) * (wPow + uPow - VPow) * (uPow + vPow - WPow)) vol = sqrt(a) vol /= b print(round(vol,4)) # Driver code if __name__ == "__main__" : # edge lengths u, v, w = 1000, 1000, 1000 U, V, W = 3, 4, 5 b = 12 findVolume(u, v, w, U, V, W, b) # This code is contributed by ANKITRAI1 |
C#
// C# implementation of above approachusing System; class GFG{// Function to find the volumestatic void findVolume(double u, double v, double w, double U, double V, double W, double b){ // Steps to calculate volume of a // Tetrahedron using formula double uPow = Math.Pow(u, 2); double vPow = Math.Pow(v, 2); double wPow = Math.Pow(w, 2); double UPow = Math.Pow(U, 2); double VPow = Math.Pow(V, 2); double WPow = Math.Pow(W, 2); double a = 4 * (uPow * vPow * wPow) - uPow * Math.Pow((vPow + wPow - UPow), 2) - vPow * Math.Pow((wPow + uPow - VPow), 2) - wPow * Math.Pow((uPow + vPow - WPow), 2) + (vPow + wPow - UPow) * (wPow + uPow - VPow) * (uPow + vPow - WPow); double vol = Math.Sqrt(a); vol /= b; Console.Write(System.Math.Round(vol, 4));}// Driver codepublic static void Main(){ // edge lengths double u = 1000, v = 1000, w = 1000; double U = 3, V = 4, W = 5; double b = 12; findVolume(u, v, w, U, V, W, b);}}// This code is contributed// by ChitraNayal |
PHP
<?php// PHP implementation of above approach// Function to find the volumefunction findVolume($u, $v, $w, $U, $V, $W, $b){ // Steps to calculate volume of // a Tetrahedron using formula $uPow = pow($u, 2); $vPow = pow($v, 2); $wPow = pow($w, 2); $UPow = pow($U, 2); $VPow = pow($V, 2); $WPow = pow($W, 2); $a = 4 * ($uPow * $vPow * $wPow) - $uPow * pow(($vPow + $wPow - $UPow), 2) - $vPow * pow(($wPow + $uPow - $VPow), 2) - $wPow * pow(($uPow + $vPow - $WPow), 2) + ($vPow + $wPow - $UPow) * ($wPow + $uPow - $VPow) * ($uPow + $vPow - $WPow); $vol = sqrt($a); $vol /= $b; echo $vol;}// Driver code// edge lengths$u = 1000;$v = 1000;$w = 1000;$U = 3;$V = 4;$W = 5;$b = 12;findVolume($u, $v, $w, $U, $V, $W, $b);// This code is contributed// by Shivi_Aggarwal ?> |
Javascript
<script>// Javascript implementation of above approach // Function to find the volumefunction findVolume(u, v, w, U, V, W, b){ // Steps to calculate volume of a // Tetrahedron using formula let uPow = Math.pow(u, 2); let vPow = Math.pow(v, 2); let wPow = Math.pow(w, 2); let UPow = Math.pow(U, 2); let VPow = Math.pow(V, 2); let WPow = Math.pow(W, 2); let a = 4 * (uPow * vPow * wPow) - uPow * Math.pow((vPow + wPow - UPow), 2) - vPow * Math.pow((wPow + uPow - VPow), 2) - wPow * Math.pow((uPow + vPow - WPow), 2) + (vPow + wPow - UPow) * (wPow + uPow - VPow) * (uPow + vPow - WPow); let vol = Math.sqrt(a); vol /= b; document.write(vol.toFixed(4));}// Driver code// Edge lengthslet u = 1000, v = 1000, w = 1000;let U = 3, V = 4, W = 5;let b = 12;findVolume(u, v, w, U, V, W, b);// This code is contributed by avanitrachhadiya2155</script> |
Output:
1999.9947
Time Complexity: O(logn) as using inbuilt pow function
Auxiliary Space: O(1)
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