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

Property:

It can be made by revolving a small circle (radius r) along a line made by a bigger circle (radius R).
It is not a polyhedron
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++

// 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; 
} 

C

// 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); 
} 

Java

// 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); 
    } 
} 

Python3

# 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); 

C#

// 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 

PHP

<?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 
?> 

Output:

Volume: 1243.568195
Surface: 829.045464

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My Personal Notes

C++

C

Java

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