圆锥台的体积和表面积的程序

给定圆锥体的截锥体的高度，高度和半径，我们必须计算圆锥体的截锥体的体积和表面积。

锥台
在几何学中，平截头体是实体(通常是圆锥体或金字塔)的一部分，位于一个或两个平行的平面之间，将其切割。
如果我们用一个平行于它的底面的平面切一个右圆锥，则该平面和底面之间的实体部分称为圆锥台。

下面给出的是右圆锥形。

右圆锥被平行于其底面的平面切割后，会产生如下所示的视锥面：

它在半径R的底部有一个圆形底座
半径为r的圆形上部
高度h
倾斜高度l

• 圆锥台的体积：

  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
  

• 圆锥台的弯曲表面积：

  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
  

• 圆锥台的总表面积：

  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
  

  例子：

  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 
  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

  输出：

  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