Given r is the radius of three equal circles touching each other. The task is to find the length of the rope tied around the circles as shown below:
Examples:
Input: r = 7
Output: 86Input: r = 14
Output: 172
Approach: As it can be clearly seen from above image, the part of the length of rope which is not touching the circle is 2r + 2r + 2r = 6r.
The part of the rope which is touching the circles make a sector of 120 degrees on each circle. Thus, three sectors of 120 degrees each can be considered as a complete one circle of 360 degrees.
Therefore, Length of rope touching the circle is 2 * PI * r where PI = 22 / 7 and r is the radius of the circle.
Hence, the total length of the rope will be ( 2 * PI * r ) + 6r.
Below is the implementation of the above approach:
C++
// C++ program to find the length// of rope#include<bits/stdc++.h>using namespace std;#define PI 3.14159265// Function to find the length// of ropefloat length_rope( float r ){ return ( ( 2 * PI * r ) + 6 * r );}// Driver codeint main(){ float r = 7; cout<<ceil(length_rope( r ))<<endl; return 0;} |
C
// C program to find the length// of rope#include <stdio.h>#define PI 3.14159265// Function to find the length// of ropefloat length_rope( float r ){ return ( ( 2 * PI * r ) + 6 * r );}// Driver codeint main(){ float r = 7; printf("%f", length_rope( r )); return 0;} |
Java
// Java code to find the length// of ropeimport java.lang.*;class GFG { static double PI = 3.14159265; // Function to find the length // of rope public static double length_rope(double r) { return ((2 * PI * r) + 6 * r); } // Driver code public static void main(String[] args) { double r = 7; System.out.println(length_rope(r)); }} |
Python3
# Python3 code to find the length# of ropePI = 3.14159265 # Function to find the length# of ropedef length_rope( r ): return ( ( 2 * PI * r ) + 6 * r ) # Driver coder = 7print( length_rope( r )) |
C#
// C# code to find the length// of ropeusing System;class GFG { static double PI = 3.14159265; // Function to find the length // of rope public static double length_rope(double r) { return ((2 * PI * r) + 6 * r); } // Driver code public static void Main() { double r = 7.0; Console.Write(length_rope(r)); }} |
PHP
<?php// PHP program to find the // length of rope$PI = 3.14159265;// Function to find the length// of ropefunction length_rope( $r ){ global $PI; return ( ( 2 * $PI * $r ) + 6 * $r );}// Driver code$r=7;echo(length_rope( $r ));?> |
Javascript
<script>// Javascript program to find the length// of ropeconst PI = 3.14159265;// Function to find the length// of ropefunction length_rope(r){ return((2 * PI * r) + 6 * r);}// Driver codelet r = 7;document.write(Math.ceil(length_rope(r)));// This code is contributed by souravmahato348</script> |
86
Time Complexity: O(1)
Auxiliary Space: O(1)
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