Percentage change in Hemisphere volume if radius is changed
Given that the radius of a hemisphere is changed by a fixed percentage so, the target is to calculate the percentage changed in the volume of the hemisphere.
Examples:
Input: r = 20%
Output: 72.80%
Input: r = 70%
Output: 391.30 %
Approach:
- Let, the radius of the hemisphere =
- Given percentage increase =
- Volume before increase =
- New radius after increase =
- So, new volume =
- Change in volume =
- Percentage increase in volume
Below is the implementation of the above approach:
CPP
// C++ program to find percentage change // in hemisphere volume wrt change in radius #include <iostream> #include <math.h> using namespace std; // Function to find the change // in hemispheric volume void new_vol( double x) { if (x > 0) { cout << "% change in the " << "volume of the hemisphere: " << pow (x, 3) / 10000 + 3 * x + (3 * pow (x, 2)) / 100 << "%" << " increase\n" ; } else if (x < 0) { cout << "% change in the " << "volume of the hemisphere: " << pow (x, 3) / 10000 + 3 * x + (3 * pow (x, 2)) / 100 << "% decrease\n" ; } else { cout << "Volume remains the same." ; } } // Driver code int main() { // Get the change in radius double x = -10.0; // Calculate the change in hemispheric volume new_vol(x); return 0; } |
Java
// Java program to find percentage change // in hemisphere volume wrt change in radius class GFG { // Function to find the change // in hemispheric volume static void new_vol( double x) { if (x > 0 ) { System.out.print( "% change in the " + "volume of the hemisphere: " + (Math.pow(x, 3 ) / 10000 + 3 * x + ( 3 * Math.pow(x, 2 )) / 100 ) + "%" + " increase\n" ); } else if (x < 0 ) { System.out.print( "% change in the " + "volume of the hemisphere: " + (Math.pow(x, 3 ) / 10000 + 3 * x + ( 3 * Math.pow(x, 2 )) / 100 ) + "% decrease\n" ); } else { System.out.print( "Volume remains the same." ); } } // Driver code public static void main(String[] args) { // Get the change in radius double x = - 10.0 ; // Calculate the change in hemispheric volume new_vol(x); } } // This code is contributed by Rajput-Ji |
Python
# Python3 program to find percentage change # in hemisphere volume wrt change in radius # Function to find the change # in hemispheric volume def new_vol(x): if (x > 0 ): print ( "% change in the volume of the hemisphere: " , pow (x, 3 ) / 10000 + 3 * x + ( 3 * pow (x, 2 )) / 100 , "% increase" ) elif (x < 0 ): print ( "% change in the volume of the hemisphere: " , pow (x, 3 ) / 10000 + 3 * x + ( 3 * pow (x, 2 )) / 100 , "% decrease" ) else : print ( "Volume remains the same." ) # Driver code # Get the change in radius x = - 10.0 # Calculate the change in hemispheric volume new_vol(x) # This code is contributed by mohit kumar 29 |
C#
// C# program to find percentage change // in hemisphere volume wrt change in radius using System; class GFG { // Function to find the change // in hemispheric volume static void new_vol( double x) { if (x > 0) { Console.Write( "% change in the " + "volume of the hemisphere: " + (Math.Pow(x, 3) / 10000 + 3 * x + (3 * Math.Pow(x, 2)) / 100) + "%" + " increase\n" ); } else if (x < 0) { Console.Write( "% change in the " + "volume of the hemisphere: " + (Math.Pow(x, 3) / 10000 + 3 * x + (3 * Math.Pow(x, 2)) / 100) + "% decrease\n" ); } else { Console.Write( "Volume remains the same." ); } } // Driver code public static void Main() { // Get the change in radius double x = -10.0; // Calculate the change in hemispheric volume new_vol(x); } } // This code is contributed by AnkitRai01 |
Javascript
// javascript program to find percentage change // in hemisphere volume wrt change in radius // Function to find the change // in hemispheric volume function new_vol(x) { if (x > 0) { document.write( "% change in the " + "volume of the hemisphere: " + (Math.pow(x, 3) / 10000 + 3 * x + (3 * Math.pow(x, 2)) / 100) + "%" + " increase\n" ); } else if (x < 0) { document.write( "% change in the " + "volume of the hemisphere: " + (Math.pow(x, 3) / 10000 + 3 * x + (3 * Math.pow(x, 2)) / 100) + "% decrease\n" ); } else { document.write( "Volume remains the same." ); } } // Driver code // Get the change in radius var x = -10.0; // Calculate the change in hemispheric volume new_vol(x); // This code is contributed by bunnyram19. |
Output:
% change in the volume of the hemisphere: -27.1% decrease
Time Complexity: O(1)
Auxiliary Space: O(1) as using only constant variables
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