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

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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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