# Program for Volume and Surface area of Frustum of Cone

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 of frustum of cone:
• ```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
```
• TotalSurface Area of frustum of cone:
• ```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 ` `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

 ` `

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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