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).
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()
{ // 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)