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 (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
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 = 3big_radius = 8slant_height = 13height = 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
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
