Program for Volume and Surface area of Frustum of Cone

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));
      }
  }
  

  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
  
  

  JavaScript

  // Function to calculate Volume of frustum of cone
  function volume(r, R, h) {
      const 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 curvedSurfaceArea(r, R, l) {
      const pi = 3.14159;
      return pi * l * (R + r);
  }
  
  // Function to calculate Total Surface area of frustum of cone
  function totalSurfaceArea(r, R, l, h) {
      const pi = 3.14159;
      return pi * l * (R + r) + pi * (r * r + R * R);
  }
  
  // Driver function
  function main() {
      const smallRadius = 3;
      const bigRadius = 8;
      const slantHeight = 13;
      const height = 12;
  
      // Printing value of volume and surface area
      console.log("Volume Of Frustum of Cone : " + volume(smallRadius, bigRadius, height));
      console.log("Curved Surface Area Of Frustum of Cone : " + curvedSurfaceArea(smallRadius, bigRadius, slantHeight));
      console.log("Total Surface Area Of Frustum of Cone : " + totalSurfaceArea(smallRadius, bigRadius, slantHeight, height));
  }
  
  // Calling the main function
  main();
  

  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
  ?>
  
  
  
  

  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".
  
  

• 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