Given a sphere of radius 
. The task is to find volume of the biggest right circular cylinder that can be inscribed within it.
Examples:
Input : R = 4 Output : 77.3495 Input : R = 5 Output : 151.073
Approach:
let r be the radius of the right circular cylinder, and h be it’s height.
Volume of the cylinder, V = ?*r2*h
Also, r2 = R2 – h2
or, V = ?*(R2 – h2)*h
or, dV/dh = ?*(R2 – 3*h2)
Setting it to zero, we get h = R/?3
So, Vmax = 2?R3/3?3
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest right circular cylinder// that can be fit within a sphere#include <bits/stdc++.h>using namespace std;// Function to find the biggest right circular cylinderfloat cyl(float R){ // radius cannot be negative if (R < 0) return -1; // volume of cylinder float V = (2 * 3.14 * pow(R, 3)) / (3 * sqrt(3)); return V;}// Driver codeint main(){ float R = 4; cout << cyl(R) << endl; return 0;} |
Java
// Java Program to find the biggest// right circular cylinder that can// be fit within a sphereimport java.io.*;class GFG{// Function to find the biggest// right circular cylinderstatic float cyl(float R){ // radius cannot be negative if (R < 0) return -1; // volume of cylinder float V = (float)((2 * 3.14 * Math.pow(R, 3)) / (3 * Math.sqrt(3))); return V;}// Driver codepublic static void main (String[] args){ float R = 4; System.out.print( cyl(R));}}// This code is contributed by anuj_67.. |
Python 3
# Python 3 Program to find the biggest # right circular cylinder that can be# fit within a sphereimport math# Function to find the biggest right # circular cylinderdef cyl(R): # radius cannot be negative if (R < 0): return -1 # volume of cylinder V = ((2 * 3.14 * math.pow(R, 3)) / (3 * math.sqrt(3))); return float(V)# Driver codeR = 4print(cyl(R))# This code is contributed# by PrinciRaj1992 |
C#
// C# Program to find the biggest// right circular cylinder that can// be fit within a sphereusing System;class GFG{// Function to find the biggest// right circular cylinderstatic float cyl(float R){ // radius cannot be negative if (R < 0) return -1; // volume of cylinder float V = (float)((2 * 3.14 * Math.Pow(R, 3)) / (3 * Math.Sqrt(3))); return V;}// Driver codepublic static void Main (){ float R = 4; Console.WriteLine( cyl(R));}}// This code is contributed by shs |
PHP
<?php// PHP Program to find the biggest right circular cylinder// that can be fit within a sphere// Function to find the biggest right circular cylinderfunction cyl($R){ // radius cannot be negative if ($R < 0) return -1; // volume of cylinder $V = (2 * 3.14 * pow($R, 3)) / (3 * sqrt(3)); return $V;}// Driver code $R = 4; echo cyl($R);// This code is contributed by shs ?> |
Javascript
<script>// javascript Program to find the biggest// right circular cylinder that can// be fit within a sphere// Function to find the biggest// right circular cylinderfunction cyl(R){ // radius cannot be negative if (R < 0) return -1; // volume of cylinder var V = ((2 * 3.14 * Math.pow(R, 3)) / (3 * Math.sqrt(3))); return V;}// Driver codevar R = 4;document.write( cyl(R).toFixed(4));// This code contributed by shikhasingrajput </script> |
Output:
77.3495
Time Complexity: O(1)
Auxiliary Space: O(1)
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