# Percentage increase in volume of the cube if a side of cube is increased by a given percentage

Given here is a cube, whose one side is increased by a given percentage. The task is to find percentage increase in the volume of the cube.**Examples:**

Input:x = 10Output:33.1%Input:x = 50Output:237.5%

**Approach**

- In a cube, all sides are equal, so,
**length = breadth = height** - let side of the cube =
**a** - given percentage increase =
**x%** - so, volume before increase =
**a^3** - after increase, new side =
**a + ax/100** - so, new volume =
**(a + ax/100)^3**=**a^3 + (ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000** - increase in volume = new volume – old volume =
**(a^3 + (ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000) – a^3**=**(ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000** - so, percentage increase in volume =
**(((ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)/a^3) * 100**=**((x/100)^3 + 3x/100 + 3x^2/10000) * 100 = x^3/10000 + 3x + 3x^2/100**

Below is the implementation of the above approach:

## C++

`// C++ program to find percentage increase` `// in the volume of the cube` `// if a side of cube is increased` `// by a given percentage` `#include <bits/stdc++.h>` `using` `namespace` `std;` `void` `newvol(` `double` `x)` `{` ` ` `cout << ` `"percentage increase "` ` ` `<< ` `"in the volume of the cube is "` ` ` `<< ` `pow` `(x, 3) / 10000 + 3 * x` ` ` `+ (3 * ` `pow` `(x, 2)) / 100` ` ` `<< ` `"%"` `<< endl;` `}` `// Driver code` `int` `main()` `{` ` ` `double` `x = 10;` ` ` `newvol(x);` ` ` `return` `0;` `}` |

## Java

`// Java program to find percentage increase` `// in the volume of the cube` `// if a side of cube is increased` `// by a given percentage` `import` `java.io.*;` `class` `GFG` `{` `static` `void` `newvol(` `double` `x)` `{` ` ` `System.out.print( ` `"percentage increase "` ` ` `+` `"in the volume of the cube is "` ` ` `+ (Math.pow(x, ` `3` `) / ` `10000` `+ ` `3` `* x` ` ` `+ (` `3` `* Math.pow(x, ` `2` `)) / ` `100` `) );` ` ` `System.out.print(` `"%"` `);` `}` `// Driver code` `public` `static` `void` `main (String[] args)` `{` ` ` `double` `x = ` `10` `;` ` ` `newvol(x);` `}` `}` `// This code is contributed by anuj_67..` |

## Python3

`# Python program to find percentage increase` `# in the volume of the cube` `# if a side of cube is increased` `# by a given percentage` `def` `newvol(x):` ` ` `print` `(` `"percentage increase"` ` ` `"in the volume of the cube is "` `,` ` ` `((x` `*` `*` `(` `3` `)) ` `/` `10000` `+` `3` `*` `x` ` ` `+` `(` `3` `*` `(x` `*` `*` `(` `2` `))) ` `/` `100` `),` `"%"` `);` `x ` `=` `10` `;` `newvol(x);` `# This code is contributed by PrinciRaj1992` |

## C#

`// C# program to find percentage increase` `// in the volume of the cube` `// if a side of cube is increased` `// by a given percentage` `using` `System;` `class` `GFG` `{` `static` `void` `newvol(` `double` `x)` `{` ` ` `Console.Write( ` `"percentage increase "` ` ` `+` `"in the volume of the cube is "` ` ` `+ (Math.Pow(x, 3) / 10000 + 3 * x` ` ` `+ (3 * Math.Pow(x, 2)) / 100) );` ` ` `Console.Write(` `"%"` `);` `}` `// Driver code` `public` `static` `void` `Main ()` `{` ` ` `double` `x = 10;` ` ` `newvol(x);` `}` `}` `// This code is contributed by anuj_67..` |

## Javascript

`<script>` `// javascript program to find percentage increase` `// in the volume of the cube` `// if a side of cube is increased` `// by a given percentage` `function` `newvol( x)` `{` ` ` `document.write(` `"percentage increase "` ` ` `+ ` `"in the volume of the cube is "` ` ` `+ (Math.pow(x, 3) / 10000 + 3 * x` ` ` `+ (3 * Math.pow(x, 2)) / 100)` ` ` `+ ` `"%"` `);` `}` `// Driver code` ` ` `let x = 10;` ` ` `newvol(x);` ` ` `// This code is contributed by gauravrajput1` `</script>` |

**Output:**

percentage increase in the volume of the cube is 33.1%

**Time Complexity:** O(log(x))

**Auxiliary Space:** O(log(x))