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Percentage increase in volume of the cube if a side of cube is increased by a given percentage
• Last Updated : 17 Mar, 2021

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 = 10
Output: 33.1%

Input: x = 50
Output: 237.5%```

Approach

• In a cube, all sides are equal, so,
• 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 ``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

 ``
Output:
`percentage increase in the volume of the cube is 33.1%`

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