how to find surface area of a cone

Calculate volume and surface area of a cone

Given slant height, height and radius of a cone, we have to calculate the volume and surface area of the cone.

Cone :
Cone is a three dimensional geometric shape. It consists of a base having the shape of a circle and a curved side (the lateral surface) ending up in a tip called the apex or vertex.

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Volume of a cone :
The volume of a cone is given by the formula –

volume = 1/3(pi * r * r * h)

where r is the radius of the circular base, and h is the height (the perpendicular distance from the base to the vertex).

Surface area of a cone :
The surface area of a cone is given by the formula –

area = pi * r * s + pi * r^2

Where r is the radius of the circular base, and s is the slant height of the cone.

Examples :

            Input            :  radius = 5 slant_height = 13 height = 12            Output            : Volume Of Cone = 314.159 Surface Area Of Cone = 282.743            Input            : radius = 6 slant_height = 10 height = 8            Output            :  Volume Of Cone = 301.593 Surface Area Of Cone = 301.593

C++

#include<iostream>

using namespace std;

float pi = 3.14159;

float volume( float r, float h)

{

return ( float (1) / float (3)) * pi *

r * r * h;

}

float surface_area( float r, float s)

{

return pi * r * s + pi * r * r;

}

int main()

{

float radius = 5;

float slant_height = 13;

float height = 12;

float vol, sur_area;

cout << "Volume Of Cone : "

<< volume(radius, height) << endl;

cout << "Surface Area Of Cone : "

<< surface_area(radius, slant_height);

return 0;

}

Java

class GFG

{

static float pi = 3 .14159f;

public static float volume( float r,

float h)

{

return ( float ) 1 / 3 * pi * h *

r * r;

}

public static float surface_area( float r,

float s)

{

return pi * r * s + pi * r * r;

}

public static void main(String args[])

{

float radius = 5 ;

float slant_height = 13 ;

float height = 12 ;

float vol, sur_area;

System.out.print( "Volume Of Cone : " );

System.out.println(volume(radius, height));

System.out.print( "Surface Area Of Cone : " );

System.out.println(surface_area(radius,

slant_height));

}

Python

import math

pi = math.pi

def volume(r, h):

return ( 1 / 3 ) * pi * r * r * h

def surfacearea(r, s):

return pi * r * s + pi * r * r

radius = float ( 5 )

height = float ( 12 )

slat_height = float ( 13 )

print ( "Volume Of Cone : " , volume(radius, height) )

print ( "Surface Area Of Cone : " , surfacearea(radius, slat_height) )

C#

using System;

class GFG

{

static float pi = 3.14159f;

public static float volume( float r,

float h)

{

return ( float )1 / 3 * pi * h *

r * r;

}

public static float surface_area( float r,

float s)

{

return pi * r * s + pi * r * r;

}

public static void Main()

{

float radius = 5;

float slant_height = 13;

float height = 12;

Console.Write( "Volume Of Cone : " );

Console.WriteLine(volume(radius,

height));

Console.Write( "Surface Area Of Cone : " );

Console.WriteLine(surface_area(radius,

slant_height));

}

PHP

<?php

function volume( $r , $h )

{

$pi = 3.14159;

return (1 / 3) * $pi * $r *

$r * $h ;

}

function surface_area( $r , $s )

{

$pi = 3.14159;

return $pi * $r * $s + $pi *

$r * $r ;

}

$radius = 5;

$slant_height = 13;

$height = 12;

echo ( "Volume Of Cone : " );

echo ( volume( $radius , $height ));

echo ( "\n" );

echo ( "Surface Area Of Cone : " );

echo ( surface_area( $radius ,

$slant_height ));

?>

Javascript

<script>

const pi = 3.14159;

function volume( r, h)

{

return ((1) / (3)) * pi *

r * r * h;

}

function surface_area( r, s)

{

return pi * r * s + pi * r * r;

}

let radius = 5;

let slant_height = 13;

let height = 12;

let vol, sur_area;

document.write( "Volume Of Cone : "

+ volume(radius, height).toFixed(2) + "<br/>" );

document.write( "Surface Area Of Cone : "

+ surface_area(radius, slant_height).toFixed(2) + "<br/>" );

</script>

Output :

Volume Of Cone : 314.159 Surface Area Of Cone : 282.743