Program to find the Volume of an irregular tetrahedron

Given the length of edges of an irregular tetrahedron. The task is to determine the volume of that tetrahedron.

Let 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 Volume of an irregular Tetrahedron in terms of its edge lengths is:
A =
\begin{vmatrix} 0 & u*u & v*v & w*w & 1 \\ u*u & 0 & W*W & V*V & 1 \\ v*v & W*W & 0 & U*U & 1 \\ w*w & V*V & W*W & 0 & 1 \\ 1 & 1 & 1 & 1 & 0 \notag \end{vmatrix}

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 above approach:

C++

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// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
#define db double
// Function to find the volume
void 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 code
int 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;
}

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// Java implementation of above approach 


  


import java.util.*; 


import java.lang.*; 


import java.io.*; 


  


  


class GFG{ 


  


// Function to find the volume 


static 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 code 


public 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); 


} 


      


} 



















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# Python 3 implementation of above approach  


  


# from math lib import everything 


from 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 



















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C#














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// C# implementation of above approach 


using System;  


  


class GFG 


{ 


  


// Function to find the volume 


static 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 code 


public 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 



















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<?php 


// PHP implementation of above approach 


  


// Function to find the volume 


function 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  


?> 



















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Output:


1999.9947







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