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📜  圆锥台体积和表面积的程序

📅  最后修改于: 2021-10-23 08:44:29             🧑  作者: Mango

给定圆锥截头体的倾斜高度、高度和半径，我们必须计算圆锥体截头体的体积和表面积。

圆锥台
在几何学中，截锥体是位于一个或两个平行平面之间的实体（通常是圆锥体或棱锥体）的一部分。
如果我们用平行于其底面的平面切割一个直圆锥，则该平面和底面之间的固体部分称为圆锥的截头体。

下面给出的是一个正圆锥。


被平行于其底面的平面切割后的正圆锥产生如下截锥体：


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
和倾斜高度 l

  • 圆锥台体积： 
    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
  • 圆锥体的曲面面积： 
    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
  • 圆锥体的总表面积： 
    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

    PHP

    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