# Percentage change in Hemisphere volume if radius is changed

• Difficulty Level : Medium
• Last Updated : 27 Mar, 2022

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 #include using namespace std; // Function to find the change// in hemispheric volumevoid 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 codeint 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 radiusclass GFG{ // Function to find the change// in hemispheric volumestatic 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 codepublic 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 volumedef 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 radiusx = -10.0 # Calculate the change in hemispheric volumenew_vol(x) # This code is contributed by mohit kumar 29

## C#

 // C# program to find percentage change// in hemisphere volume wrt change in radiususing 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(log(x))

Auxiliary Space: O(log(x))

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