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` |

**Output:**

% change in the volume of the hemisphere: -27.1% decrease

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