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Calculate volume and surface area of Torus

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  • Last Updated : 21 Jun, 2022

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++




// C++ program to calculate volume
// and surface area of Torus
#include<bits/stdc++.h>
using namespace std;
 
int 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;
    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()
{
    // 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;
    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
# radius 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
 
// radius 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
?>

Javascript




<script>
 
// Javascript program to calculate volume
// and surface area of Torus
 
// radius of inner circle
var r = 3;
 
// distance from origin to center of inner circle
// radius of black circle in figure
var R = 7;
 
// Value of Pi
var pi = 3.14159;
var Volume = 0;
Volume = 2 * pi * pi * R * r * r;
document.write("Volume: " + Volume + "<br>");
 
var Surface = 4 * pi * pi * R * r;
document.write("Surface: " + Surface);
 
</script>

Output: 

Volume: 1243.568195
Surface: 829.045464

 

Time complexity : O(1) 
Auxiliary Space : O(1)


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