# Program to check if water tank overflows when n solid balls are dipped in the water tank

Given the dimensions of cylindrical water tank, spherical solid balls and the amount of water present in the tank check if water tank will overflow when balls are dipped in the water tank. **Examples : **

input : H = 10, r = 5 h = 5 N = 2, R = 2 output : Not in overflow state Explanation : water tank capacity = 3.14 * r * r * H = 3.14 * 5 * 5 * 10 = 785 volume of water in tank = 3.14 * r * r * h = 3.14 * 5 * 5 * 5 = 392.5 Volume of balls = N * (4/3) * 3.14 * R * R * R = 2 * (4/3) * 3.14 * 2 * 2 * 2 = 67.02 Total volume of water + dip balls = 392.5 + 67.02 = 459.52 Total volume (459.02) < tank capacity (785) So, there is no overflow in tank input : H = 5, r = 3 h = 3 N = 3, R = 2 output : Overflow Explanation: water tank capacity = 3.14 * r * r * H = 3.14 * 3 * 3 * 5 = 141.3 volume of water in tank = 3.14 * r * r * h = 3.14 * 3 * 3 * 3 = 84.78 volume of balls = N * (4/3) * 3.14 * R * R * R = 3 * (4/3) * 3.14 * 2 * 2 * 2 = 100.48 Total volume of water + dip balls = 84.78 + 100.48 = 185.26 Total volume (185.26) > tank capacity (141.3) So, tank will overflow

**Approach:**

When solid balls are dipped in water, level of water increases, hence volume of water will also increase.

Increasing in water volume = Total volume of dip balls

Volume of Cylinder = 3.14 * r * r * h

where: r: radius of tank

h: height of tank

Number of balls are n

Balls have shape of Sphere

Volume of Sphere = (4/3) * 3.14 * R * R * R

Where R: Sphere’s(solid ball) radius

After dipping all balls, if the total volume of water and all balls is less than or equal to the total volume of tank capacity then there will no overflow in tank, otherwise there will be overflow.

Below is the implementation of above approach:

## C++

`// C++ Program to check if water tank` `// overflows when n solid balls are` `// dipped in the water tank` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// function to find if tak will` `// overflow or not` `void` `overflow(` `int` `H, ` `int` `r, ` `int` `h,` ` ` `int` `N, ` `int` `R)` `{` ` ` `// cylinder capacity` ` ` `float` `tank_cap = 3.14 * r * r * H;` ` ` `// volume of water in tank` ` ` `float` `water_vol = 3.14 * r * r * h;` ` ` `// volume of n balls` ` ` `float` `balls_vol = N * (4 / 3) * 3.14 * R * R * R;` ` ` `// total volume of water` ` ` `// and n dipped balls` ` ` `float` `vol = water_vol + balls_vol;` ` ` `/* condition to check if tank is in` ` ` `overflow state or not */` ` ` `if` `(vol > tank_cap) {` ` ` `cout << ` `"Overflow"` `<< endl;` ` ` `}` ` ` `else` `{` ` ` `cout << ` `"Not in overflow state"` ` ` `<< endl;` ` ` `}` `}` `// main function` `int` `main()` `{` ` ` `// giving dimensions` ` ` `int` `H = 10, r = 5, h = 5,` ` ` `N = 2, R = 2;` ` ` `// calling function` ` ` `overflow(H, r, h, N, R);` ` ` `return` `0;` `}` |

## Java

`// JAVA Code for Program to check if` `// water tank overflows` `import` `java.util.*;` `class` `GFG {` ` ` `// function to find if tak will` ` ` `// overflow or not` ` ` `static` `void` `overflow(` `int` `H, ` `int` `r, ` `int` `h,` ` ` `int` `N, ` `int` `R)` ` ` `{` ` ` `// cylinder capacity` ` ` `double` `tank_cap = ` `3.14` `* r * r * H;` ` ` `// volume of water in tank` ` ` `double` `water_vol = ` `3.14` `* r * r * h;` ` ` `// volume of n balls` ` ` `double` `balls_vol = N * (` `4` `/ ` `3` `) * ` `3.14` `* R * R * R;` ` ` `// total volume of water` ` ` `// and n dipped balls` ` ` `double` `vol = water_vol + balls_vol;` ` ` `/* condition to check if tank is in` ` ` `overflow state or not */` ` ` `if` `(vol > tank_cap) {` ` ` `System.out.println(` `"Overflow"` `);` ` ` `}` ` ` `else` `{` ` ` `System.out.println(` `"Not in overflow state"` `);` ` ` `}` ` ` `}` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// giving dimensions` ` ` `int` `H = ` `10` `, r = ` `5` `, h = ` `5` `,` ` ` `N = ` `2` `, R = ` `2` `;` ` ` `// calling function` ` ` `overflow(H, r, h, N, R);` ` ` `}` `}` `// This code is contributed by Arnav Kr. Mandal.` |

## Python3

`# Python code to check if water tank` `# overflows when n solid balls are` `# dipped in the water tank` `# function to find if tak will` `# overflow or not` `def` `overflow( H, r, h, N, R ):` ` ` `# cylinder capacity` ` ` `tank_cap ` `=` `3.14` `*` `r ` `*` `r ` `*` `H` ` ` ` ` `# volume of water in tank` ` ` `water_vol ` `=` `3.14` `*` `r ` `*` `r ` `*` `h` ` ` ` ` `# volume of n balls` ` ` `balls_vol ` `=` `N ` `*` `(` `4` `/` `3` `) ` `*` `3.14` `*` `R ` `*` `R ` `*` `R` ` ` ` ` `# total volume of water` ` ` `# and n dipped balls` ` ` `vol ` `=` `water_vol ` `+` `balls_vol` ` ` ` ` `# condition to check if tank is in` ` ` `# overflow state or not` ` ` `if` `vol > tank_cap:` ` ` `print` `(` `"Overflow"` `)` ` ` `else` `:` ` ` `print` `(` `"Not in overflow state"` `)` `# Driver code` `# giving dimensions` `H ` `=` `10` `r ` `=` `5` `h ` `=` `5` `N ` `=` `2` `R ` `=` `2` `# calling function` `overflow (H, r, h, N, R)` `# This code is contributed by "Sharad_Bhardwaj".` |

## C#

`// C# Code for Program to check if` `// water tank overflows` `using` `System;` `class` `GFG {` ` ` `// function to find if tak will` ` ` `// overflow or not` ` ` `static` `void` `overflow(` `int` `H, ` `int` `r, ` `int` `h,` ` ` `int` `N, ` `int` `R)` ` ` `{` ` ` `// cylinder capacity` ` ` `double` `tank_cap = 3.14 * r * r * H;` ` ` `// volume of water in tank` ` ` `double` `water_vol = 3.14 * r * r * h;` ` ` `// volume of n balls` ` ` `double` `balls_vol = N * (4 / 3) * 3.14 * R * R * R;` ` ` `// total volume of water` ` ` `// and n dipped balls` ` ` `double` `vol = water_vol + balls_vol;` ` ` `/* condition to check if tank is in` ` ` `overflow state or not */` ` ` `if` `(vol > tank_cap) {` ` ` `Console.WriteLine(` `"Overflow"` `);` ` ` `}` ` ` `else` `{` ` ` `Console.WriteLine(` `"Not in overflow state"` `);` ` ` `}` ` ` `}` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `// giving dimensions` ` ` `int` `H = 10, r = 5, h = 5,` ` ` `N = 2, R = 2;` ` ` `// calling function` ` ` `overflow(H, r, h, N, R);` ` ` `}` `}` `// This code is contributed by vt_M.` |

## PHP

`<?php` `// PHP Program to check if water tank` `// overflows when n solid balls are` `// dipped in the water tank` `// function to find if tank` `// will overflow or not` `function` `overflow(` `$H` `, ` `$r` `, ` `$h` `,` ` ` `$N` `, ` `$R` `)` `{` ` ` `// cylinder capacity` ` ` `$tank_cap` `= 3.14 * ` `$r` `*` ` ` `$r` `* ` `$H` `;` ` ` ` ` `// volume of water in tank` ` ` `$water_vol` `= 3.14 * ` `$r` `*` ` ` `$r` `* ` `$h` `;` ` ` ` ` `// volume of n balls` ` ` `$balls_vol` `= ` `$N` `* (4/3) *` ` ` `3.14 * ` `$R` `*` ` ` `$R` `* ` `$R` `;` ` ` ` ` `// total volume of water` ` ` `// and n dipped balls` ` ` `$vol` `= ` `$water_vol` `+ ` `$balls_vol` `;` ` ` `// condition to check if tank` ` ` `// is in overflow state or not` ` ` `if` `(` `$vol` `> ` `$tank_cap` `)` ` ` `{` ` ` `echo` `"Overflow"` `, ` `"\n"` `;` ` ` `}` ` ` `else` ` ` `{` ` ` `echo` `"Not in overflow state"` `, ` `"\n"` `;` ` ` ` ` `}` `}` `// Driver Code` `// giving dimensions` `$H` `= 10; ` `$r` `= 5; ` `$h` `= 5;` `$N` `= 2; ` `$R` `= 2;` `// calling function ` `overflow (` `$H` `, ` `$r` `, ` `$h` `, ` `$N` `, ` `$R` `);` ` ` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` `// JavaScript program for Program to check if` `// water tank overflows` ` ` `// function to find if tak will` ` ` `// overflow or not` ` ` `function` `overflow(H, r, h,` ` ` `N, R)` ` ` `{` ` ` `// cylinder capacity` ` ` `let tank_cap = 3.14 * r * r * H;` ` ` ` ` `// volume of water in tank` ` ` `let water_vol = 3.14 * r * r * h;` ` ` ` ` `// volume of n balls` ` ` `let balls_vol = N * (4 / 3) * 3.14 * R * R * R;` ` ` ` ` `// total volume of water` ` ` `// and n dipped balls` ` ` `let vol = water_vol + balls_vol;` ` ` ` ` `/* condition to check if tank is in` ` ` `overflow state or not */` ` ` `if` `(vol > tank_cap) {` ` ` `document.write(` `"Overflow"` `);` ` ` `}` ` ` `else` `{` ` ` `document.write(` `"Not in overflow state"` `);` ` ` `}` ` ` `} ` `// Driver Code` ` ` `// giving dimensions` ` ` `let H = 10, r = 5, h = 5,` ` ` `N = 2, R = 2;` ` ` ` ` `// calling function` ` ` `overflow(H, r, h, N, R);` `// This code is contributed by chinmoy1997pal.` `</script>` |

**Output :**

Not in overflow state

**Time Complexity: **O(1)

**Auxiliary Space:** O(1)