Calculate volume and surface area of Torus

This article is about the surface and mathematical concept of a torus.
A 3D shape made by revolving a small circle (radius r) along a line made by a bigger circle (radius R).

Torus

Torus

Property:

  1. It can be made by revolving a small circle (radius r) along a line made by a bigger circle (radius R).
  2. It is not a polyhedron
  3. It has no vertices or edges
  • Surface Area
    The surface area of a Torus is given by the formula –



    Surface Area = 4 × Pi^2 × R × r

    Where r is the radius of the small circle and R is the radius of bigger circle and Pi is constant Pi=3.14159.

  • Volume
    The volume of a cone is given by the formula –

    Volume = 2 × Pi^2 × R × r^2

    Where r is the radius of the small circle and R is the radius of bigger circle and Pi is constant Pi=3.14159.

Examples:

Input : r=3, R=7
Output :
     Volume: 1243.568195
     Surface: 829.045464

C++

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// C++ program to calculate volume
// and surface area of Torus
#include<bits/stdc++.h>
using namespace std;
  
int main()
{
    // radus of inner circle
    double r = 3;
  
    // distance from origin to center of inner circle
    // radius of black circle in figure
    double R = 7;
  
    // Value of Pi
    float pi = (float)3.14159;
    double Volume = 0;
    Volume = 2 * pi * pi * R * r * r;
    cout<<"Volume: "<<Volume<<endl;
  
    double Surface = 4 * pi * pi * R * r;
    cout<<"Surface: "<<Surface<<endl;
}

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// C program to calculate volume  


// and surface area of Torus 


#include <stdio.h> 


int main() 


{ 


    // radus of inner circle 


    double r = 3; 


  


    // distance from origin to center of inner circle 


    // radius of black circle in figure 


    double R = 7; 


  


    // Value of Pi 


    float pi = (float)3.14159; 


    double Volume = 0; 


    Volume = 2 * pi * pi * R * r * r; 


    printf("Volume: %f", Volume); 


  


    double Surface = 4 * pi * pi * R * r; 


    printf("\nSurface: %f", Surface); 


} 



















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Java














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// Java program to calculate volume  


// and surface area of Torus 


class Test { 


  


    public static void main(String args[]) 


    { 


  


        // radius of inner circle 


        double r = 3; 


  


        // distance from origin to center of inner circle 


        // radius of black circle in figure 


        double R = 7; 


  


        // Value of Pi 


        float pi = (float)3.14159; 


        double Volume = 0; 


        Volume = 2 * pi * pi * R * r * r; 


        System.out.printf("Volume: %f", Volume); 


  


        double Surface = 4 * pi * pi * R * r; 


        System.out.printf("\nSurface: %f", Surface); 


    } 


} 



















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Python3














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# Python3 program to calculate volume 


# and surface area of Torus 


# radus of inner circle 


r = 3


  


# distance from origin to center of inner circle 


# radius of black circle in figure 


R = 7


  


# Value of Pi 


pi = 3.14159


Volume = (float)(2 * pi * pi * R * r * r); 


print("Volume: ", Volume); 


Surface = (float)(4 * pi * pi * R * r); 


print("Surface: ", Surface); 



















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C#














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// C# program to calculate volume  


// and surface area of Torus  


using System; 


  


class GFG  


{  


      


// Driver Code 


public static void Main()  


{  


  


    // radius of inner circle  


    double r = 3;  


  


    // distance from origin to center  


    // of inner circle radius of black 


    // circle in figure  


    double R = 7;  


  


    // Value of Pi  


    float pi = (float)3.14159;  


    double Volume = 0;  


    Volume = 2 * pi * pi * R * r * r;  


    Console.WriteLine("Volume: {0}", Volume);  


  


    double Surface = 4 * pi * pi * R * r;  


    Console.WriteLine("Surface: {0}", Surface);  


}  


}  


  


// This code is contributed by Soumik 



















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PHP














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<?php 


// PHP program to calculate volume  


// and surface area of Torus  


  


// radus of inner circle  


$r = 3;  


  


// distance from origin to center  


// of inner circle radius of black 


// circle in figure  


$R = 7;  


  


// Value of Pi  


$pi = (float)3.14159;  


$Volume = 0;  


$Volume = 2 * $pi * $pi * $R * $r * $r;  


  


echo "Volume: ", $Volume, "\n";  


  


$Surface = 4 * $pi * $pi * $R * $r;  


  


echo "Surface: ", $Surface, "\n";  


      


// This code is contributed by ajit 


?> 



















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Output:


Volume: 1243.568195
Surface: 829.045464






          
          
          
          

            

    

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