Largest cube that can be inscribed within a right circular cone

Namachila November 19, 2025

0 0 3 minutes read

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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