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# Percentage increase in volume of the sphere if radius is increased by a given percentage

• Last Updated : 09 Sep, 2022

Given here is a sphere, whose radius is increased by a given percentage. The task is to find the percentage increase in the volume of the sphere.
Examples:

```Input: x = 10
Output: 33.1%

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

Approach

• Let, the radius of the sphere = a
• given percentage increase = x%
• volume before increase = 4/3*πa^3
• new radius after increase = a + ax/100
• so, new volume = 4/3*π(a^3 + (ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)
• change in volume = 4/3*π((ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)
• percentage increase in volume = (4/3*π*((ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)/4/3*π*a^3) * 100 = x^3/10000 + 3x + 3x^2/100 ## C++

 `// C++ program to find percentage increase``// in the volume of the sphere``// if radius is increased by a given percentage` `#include ``using` `namespace` `std;` `void` `newvol(``double` `x)``{``    ``cout << ``"percentage increase in the"``         ``<< ``" volume of the sphere 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 sphere``// if radius 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 sphere is "``        ``+( Math.pow(x, ``3``) / ``10000` `+ ``3` `* x``                ``+ (``3` `* Math.pow(x, ``2``)) / ``100``)``        ``+ ``"%"``);``}` `// Driver code``public` `static` `void` `main (String[] args)``{``        ``double` `x = ``10``;``    ``newvol(x);``}``}` `// This code is contributed by anuj_67..`

## Python3

 `# Python3 program to find percentage increase``# in the volume of the sphere``# if radius is increased by a given percentage` `def` `newvol(x):` `    ``print``(``"percentage increase in the"``        ``" volume of the sphere is "``        ``,``pow``(x, ``3``) ``/` `10000` `+` `3` `*` `x``                ``+` `(``3` `*` `pow``(x, ``2``)) ``/` `100``            ``,``"%"``)` `# Driver code``x ``=` `10.0``newvol(x)` `# This code is contributed mohit kumar 29`

## C#

 `// C# program to find percentage increase``// in the volume of the sphere``// if radius is increased by a given percentage``using` `System;` `class` `GFG``{` `static` `void` `newvol(``double` `x)``{``    ``Console.WriteLine( ``"percentage increase in the"``        ``+ ``" volume of the sphere is "``        ``+( Math.Pow(x, 3) / 10000 + 3 * x``                ``+ (3 * Math.Pow(x, 2)) / 100)``        ``+ ``"%"``);``}` `// 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 sphere is 33.1%`

Time Complexity: O(1)

Auxiliary Space: O(1) since using constant variables

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