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 = 10
Output: 33.1%

Input: x = 50
Output: 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

$<strong>Percentage increase in the volume = (given percentage)^3/10000 + 3*given percentage + 3*(given percentage)^2/100</strong>$

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.. 

Output:

percentage increase in the volume of the cube is 33.1%

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