Given a semicircle with radius R, which inscribes a rectangle of length L and breadth B, which in turn inscribes a circle of radius r. The task is to find the area of the circle with radius r.
Examples:
Input : R = 2 Output : 1.57 Input : R = 5 Output : 9.8125
Approach:
We know the biggest rectangle that can be inscribed within the semicircle has, length, l=?2R/2 &
breadth, b=R/?2(Please refer)
Also, the biggest circle that can be inscribed within the rectangle has radius, r=b/2=R/2?2(Please refer)
So area of the circle, A=?*r^2=?(R/2?2)^2
C++
// C++ Program to find the area of the circle // inscribed within the rectangle which in turn // is inscribed in a semicircle #include <bits/stdc++.h> using namespace std;
// Function to find the area of the circle float area( float r)
{ // radius cannot be negative
if (r < 0)
return -1;
// area of the circle
float area = 3.14 * pow (r / (2 * sqrt (2)), 2);
return area;
} // Driver code int main()
{ float a = 5;
cout << area(a) << endl;
return 0;
} |
Java
// Java Program to find the area of the circle // inscribed within the rectangle which in turn // is inscribed in a semicircle import java.io.*;
class GFG {
// Function to find the area of the circle static float area( float r)
{ // radius cannot be negative
if (r < 0 )
return - 1 ;
// area of the circle
float area = ( float )( 3.14 * Math.pow(r / ( 2 * Math.sqrt( 2 )), 2 ));
return area;
} // Driver code public static void main (String[] args) {
float a = 5 ;
System.out.println( area(a));
}
} // This code is contributed by ajit
|
Python3
# Python 3 Program to find the # area of the circle inscribed # within the rectangle which in # turn is inscribed in a semicircle from math import pow , sqrt
# Function to find the area # of the circle def area(r):
# radius cannot be negative
if (r < 0 ):
return - 1
# area of the circle
area = 3.14 * pow (r / ( 2 * sqrt( 2 )), 2 );
return area;
# Driver code if __name__ = = '__main__' :
a = 5
print ( "{0:.6}" . format (area(a)))
# This code is contributed By # Surendra_Gangwar |
C#
// C# Program to find the area of // the circle inscribed within the // rectangle which in turn is // inscribed in a semicircle using System;
class GFG
{ // Function to find the area // of the circle static float area( float r)
{ // radius cannot be negative
if (r < 0)
return -1;
// area of the circle
float area = ( float )(3.14 * Math.Pow(r /
(2 * Math.Sqrt(2)), 2));
return area;
} // Driver code static public void Main (String []args)
{ float a = 5;
Console.WriteLine(area(a));
} } // This code is contributed // by Arnab Kundu |
PHP
<?php // PHP Program to find the area // of the circle inscribed within // the rectangle which in turn // is inscribed in a semicircle // Function to find the area // of the circle function area( $r )
{ // radius cannot be negative
if ( $r < 0)
return -1;
// area of the circle
$area = 3.14 * pow( $r /
(2 * sqrt(2)), 2);
return $area ;
} // Driver code $a = 5;
echo area( $a );
// This code is contributed by mits |
Javascript
<script> // javascript Program to find the area of the circle // inscribed within the rectangle which in turn // is inscribed in a semicircle // Function to find the area of the circle function area(r)
{ // radius cannot be negative
if (r < 0)
return -1;
// area of the circle
var area = (3.14 * Math.pow(r / (2 * Math.sqrt(2)), 2));
return area;
} // Driver code var a = 5;
document.write( area(a).toFixed(6)); // This code contributed by shikhasingrajput </script> |
Output:
9.8125
Time Complexity: O(1)
Auxiliary Space: O(1)