 Open in App
Not now

# 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

My Personal Notes arrow_drop_up
Related Articles