Dada la altura inclinada, la altura y el radio de un tronco de cono, tenemos que calcular el volumen y el área de superficie del tronco de un cono.
Frusto de cono
En geometría, un tronco de cono es la porción de un sólido (normalmente un cono o una pirámide) que se encuentra entre uno o dos planos paralelos que lo cortan.
Si cortamos un cono circular recto por un plano paralelo a su base, la parte del sólido entre este plano y la base se conoce como tronco de cono.
A continuación se muestra un cono circular recto.
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
- Volumen del tronco de cono:
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 (CSA) = pi * l(R + r) where r = radius of smaller circle R = radius of bigger circle l = slant height of the frustum
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
Ejemplos:
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
?>
Producción:
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
Publicación traducida automáticamente
Artículo escrito por Arushi Dhamija y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA