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Program for Volume and Surface area of Frustum of Cone
  • Last Updated : 23 Apr, 2018

Given slant height, height and radius of a frustum of a cone, we have to calculate the volume and surface area of the frustum of a cone.

Frustum of cone
In geometry, a frustum is the portion of a solid (normally a cone or pyramid) that lies between one or two parallel planes cutting it.
If we cut a right circular cone by a plane parallel to its base, the portion of the solid between this plane and the base is known as the frustum of a cone.

Given below is a right circular cone.


The right circular cone after being cut by a plane parallel to its base results in a frustum as follows:


which has a circular base at bottom of radius R
circular upper portion with radius r
height h
and slant height l



  • Volume of frustum of cone:
    Volume (V) = 1/3 * pi * h(r2 + R2 + r*R)
    
    where
    r = radius of smaller circle
    R = radius of bigger circle (or radius of base of the cone)
    h = height of the frustum
    
  • Curved Surface Area of frustum of cone:
    Curved Surface Area (CSA) = pi * l(R + r)
    
    where
    r = radius of smaller circle
    R = radius of bigger circle
    l = slant height of the frustum
    
  • TotalSurface Area of frustum of cone:
    Total Surface Area (TSA) = pi * l(R + r) + pi(R2 + r2)
    
    where
    r = radius of smaller circle
    R = radius of bigger circle
    l = slant height of frustum
    

    Examples:

    Input : Radius of smaller circle = 3
            Radius of bigger circle = 8
            Height of frustum = 12
            Slant height of frustum = 13
    Output :
    Volume Of Frustum of Cone : 1218.937
    Curved Surface Area Of Frustum of Cone : 449.24738
    Total Surface Area Of Frustum of Cone : 678.58344
    
    
    Input : Radius of smaller circle = 7
            Radius of bigger circle = 10
            Height of frustum = 4
            Slant height of frustum = 5
    
    Output :
    Volume Of Frustum of Cone : 917.34436
    Curved Surface Area Of Frustum of Cone : 267.03516
    Total Surface Area Of Frustum of Cone : 735.1321
    

    C++




    // CPP program to calculate Volume and
    // Surface area of frustum of cone
    #include <iostream>
    using namespace std;
      
    float pi = 3.14159;
      
    // Function to calculate Volume of frustum of cone
    float volume(float r, float R, float h)
    {
        return (float(1) / float(3)) * pi * h *
                        (r * r + R * R + r * R);
    }
      
    // Function to calculate Curved Surface area of
    // frustum of cone
    float curved_surface_area(float r, float R, float l)
    {
        return pi * l * (R + r);
    }
      
    // Function to calculate Total Surface area of 
    // frustum of cone
    float total_surface_area(float r, float R, float l, 
                                               float h)
    {
        return pi * l * (R + r) + pi * (r * r + R * R);
    }
      
    // Driver function
    int main()
    {
        float small_radius = 3;
        float big_radius = 8;
        float slant_height = 13;
        float height = 12;
      
        // Printing value of volume and surface area
        cout << "Volume Of Frustum of Cone : "
             << volume(small_radius, big_radius, height) 
             << endl;
      
        cout << "Curved Surface Area Of Frustum of Cone : "
             << curved_surface_area(small_radius, big_radius, 
                                     slant_height) << endl;
      
        cout << "Total Surface Area Of Frustum of Cone : "
             << total_surface_area(small_radius, big_radius, 
                                     slant_height, height);
        return 0;
    }

    Java




    // Java program to calculate Volume and Surface area
    // of frustum of cone
      
    public class demo {
      
        static float pi = 3.14159f;
      
        // Function to calculate Volume of frustum of cone
        public static float volume(float r, float R, float h)
        {
            return (float)1 / 3 * pi * h * (r * r + R * R +
                                                    r * R);
        }
      
        // Function to calculate Curved Surface area of
        // frustum of cone
        public static float curved_surface_area(float r, 
                                       float R, float l)
        {
            return pi * l * (R + r);
        }
      
        // Function to calculate Total Surface area of 
        // frustum of cone
        public static float total_surface_area(float r, 
                             float R, float l, float h)
        {
            return pi * l * (R + r) + pi * (r * r + R * R);
        }
      
        // Driver function
        public static void main(String args[])
        {
            float small_radius = 3;
            float big_radius = 8;
            float slant_height = 13;
            float height = 12;
      
        // Printing value of volume and surface area
            System.out.print("Volume Of Frustum of Cone : ");
            System.out.println(volume(small_radius, 
                                big_radius, height));
      
            System.out.print("Curved Surface Area Of"
                                " Frustum of Cone : ");
            System.out.println(curved_surface_area(small_radius,
                                      big_radius, slant_height));
            System.out.print("Total Surface Area Of"
                    " Frustum of Cone : ");
      
            System.out.println(total_surface_area(small_radius, 
                            big_radius, slant_height, height));
        }
    }

    Python3




    # Python3 code to calculate 
    # Volume and Surface area of
    # frustum of cone
    import math
      
    pi = math.pi
      
    # Function to calculate Volume
    # of frustum of cone
    def volume( r , R , h ):
        return 1 /3 * pi * h * (r 
                * r + R * R + r * R)
      
    # Function to calculate Curved 
    # Surface area of frustum of cone
    def curved_surface_area( r , R , l ):
        return pi * l * (R + r)
      
    # Function to calculate Total  
    # Surface area of frustum of cone
    def total_surface_area( r , R , l , h ):
        return pi * l * (R + r) + pi * (r
                                * r + R * R)
          
    # Driver Code
    small_radius = 3
    big_radius = 8
    slant_height = 13
    height = 12
      
    # Printing value of volume 
    # and surface area
    print("Volume Of Frustum of Cone : "
                                    ,end='')
    print(volume(small_radius, big_radius,
                                    height))
      
    print("Curved Surface Area Of Frustum"+
                        " of Cone : ",end='')
    print(curved_surface_area(small_radius,
                    big_radius,slant_height))
      
    print("Total Surface Area Of Frustum"+
                        " of Cone : ",end='')
    print(total_surface_area(small_radius, 
            big_radius,slant_height, height))
      
    # This code is contributed by "Sharad_Bhardwaj".

    C#




    // C# program to calculate Volume and 
    // Surface area of frustum of cone
    using System;
      
    public class demo {
      
        static float pi = 3.14159f;
      
        // Function to calculate 
        // Volume of frustum of cone
        public static float volume(float r, float R, float h)
        {
            return (float)1 / 3 * pi * h * (r * r + R * 
                                            R + r * R);
        }
      
        // Function to calculate Curved
        // Surface area of frustum of cone
        public static float curved_surface_area(float r, 
                                    float R, float l)
        {
            return pi * l * (R + r);
        }
      
        // Function to calculate Total
        // Surface area of frustum of cone
        public static float total_surface_area(float r, float R, 
                                               float l, float h)
        {
            return pi * l * (R + r) + pi *
                        (r * r + R * R);
        }
      
        // Driver function
        public static void Main()
        {
            float small_radius = 3;
            float big_radius = 8;
            float slant_height = 13;
            float height = 12;
      
        // Printing value of volume 
        // and surface area
        Console.Write("Volume Of Frustum of Cone : ");
          
        Console.WriteLine(volume(small_radius, 
                        big_radius, height));
      
        Console.Write("Curved Surface Area Of"
                         " Frustum of Cone : ");
                           
        Console.WriteLine(curved_surface_area(small_radius,
                                big_radius, slant_height));
                                  
        Console.Write("Total Surface Area Of"
                        " Frustum of Cone : ");
      
        Console.WriteLine(total_surface_area(small_radius, 
                        big_radius, slant_height, height));
        }
    }
      
    // This article is contributed by vt_m

    PHP




    <?php
    // PHP program to calculate Volume and
    // Surface area of frustum of cone
      
    // Function to calculate 
    // Volume of frustum of cone
    function volume($r, $R, $h)
    {
        $pi = 3.14159;
        return (1 / (3)) * $pi * $h *
               ($r * $r + $R * $R + $r * $R);
    }
      
    // Function to calculate Curved 
    // Surface area of frustum of cone
    function curved_surface_area($r, $R, $l)
    {
        $pi = 3.14159;
        return $pi * $l * ($R + $r);
    }
      
    // Function to calculate Total Surface 
    // area of  frustum of cone
    function total_surface_area( $r, $R, $l, $h)
    {
        $pi = 3.14159;
        return ($pi * $l * ($R + $r) + 
                $pi * ($r * $r + $R * $R));
    }
      
        // Driver Code
        $small_radius = 3;
        $big_radius = 8;
        $slant_height = 13;
        $height = 12;
      
        // Printing value of volume 
        // and surface area
        echo("Volume Of Frustum of Cone : ");
        echo(volume($small_radius
                    $big_radius
                    $height)); 
        echo("\n");
      
        echo("Curved Surface Area Of Frustum of Cone : ");
        echo (curved_surface_area($small_radius
                                  $big_radius ,
                                  $slant_height));
        echo("\n");
      
        echo("Total Surface Area Of Frustum of Cone : ");
        echo(total_surface_area($small_radius
                                $big_radius
                                $slant_height
                                $height));
          
    // This code is contributed by vt_m
    ?>

    Output:

    Volume Of Frustum of Cone : 1218.937
    Curved Surface Area Of Frustum of Cone : 449.24738
    Total Surface Area Of Frustum of Cone : 678.58344
    

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