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
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