Given a right circular cone of radius r and perpendicular height h. We have to find the side length of the biggest cube that can be inscribed within it.
Examples:
Input : h = 5, r = 6 Output : 3.14613 Input : h = 8, r = 12 Output : 5.43698
Approach:
Let, side of the cube = a.
From the diagram, we can clearly understand using the properties of triangles: BC/AB = DE/AD.
Therefore,
r/h = (a/?2)/(h-a) or, a = h*r?2/(h+?2*r)
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest cube // inscribed within a right circular cone #include <bits/stdc++.h> using namespace std;
// Function to find the side of the cube float cubeSide( float h, float r)
{ // height and radius cannot be negative
if (h < 0 && r < 0)
return -1;
// side of the cube
float a = (h * r * sqrt (2)) / (h + sqrt (2) * r);
return a;
} // Driver code int main()
{ float h = 5, r = 6;
cout << cubeSide(h, r) << endl;
return 0;
} |
Java
// Java Program to find the biggest cube // which can be inscribed within a right circular cone import java.io.*;
class GFG {
// Function to find the side of the cube static float cube( float h, float r)
{ // height and radius cannot be negative
if (h < 0 && r < 0 )
return - 1 ;
// side of the cube
float a = (h * r * ( float )Math.sqrt( 2 )) / (h + ( float )Math.sqrt( 2 ) * r);
return a;
} // Driver code public static void main (String[] args) {
float h = 5 , r = 6 ;
System.out.println( cube(h, r));
}
} // this article is contributed by Ishwar Gupta |
Python 3
# Python3 Program to find the biggest cube # inscribed within a right circular cone import math
# Function to find the side of the cube def cubeSide(h, r):
# height and radius cannot
# be negative
if (h < 0 and r < 0 ):
return - 1
# side of the cube
a = ((h * r * math.sqrt( 2 )) /
(h + math.sqrt( 2 ) * r))
return a
# Driver code h = 5 ; r = 6 ;
print (cubeSide(h, r), "\n" )
# This code is contributed # by Akanksha Rai |
C#
// C# Program to find the // biggest cube which can be // inscribed within a right // circular cone using System;
class GFG
{ // Function to find the side // of the cube static float cube( float h, float r)
{ // height and radius cannot be negative if (h < 0 && r < 0)
return -1;
// side of the cube float a = (h * r * ( float )Math.Sqrt(2)) /
(h + ( float )Math.Sqrt(2) * r);
return a;
} // Driver code public static void Main ()
{ float h = 5, r = 6;
Console.Write( cube(h, r));
} } // This code is contributed // by 29AjayKumar |
PHP
<?php // PHP Program to find the biggest cube // inscribed within a right circular cone // Function to find the side of the cube function cubeSide( $h , $r )
{ // height and radius cannot
// be negative
if ( $h < 0 && $r < 0)
return -1;
// side of the cube
$a = ( $h * $r * sqrt(2)) /
( $h + sqrt(2) * $r );
return $a ;
} // Driver code $h = 5;
$r = 6;
echo cubeSide( $h , $r );
// This code is contributed // by Shivi_Aggarwal ?> |
Javascript
<script> // javascript Program to find the biggest cube // which can be inscribed within a right circular cone // Function to find the side of the cube function cube(h , r)
{ // height and radius cannot be negative
if (h < 0 && r < 0)
return -1;
// side of the cube
var a = (h * r * Math.sqrt(2)) / (h + Math.sqrt(2) * r);
return a;
} // Driver code var h = 5, r = 6;
document.write( cube(h, r).toFixed(5)); // This code is contributed by 29AjayKumar </script> |
Output:
3.14613
Time Complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.
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