Percentage increase in volume of the cube if a side of cube is increased by a given percentage
Last Updated :
09 Sep, 2022
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
Below is the implementation of the above approach:
C++
#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;
}
int main()
{
double x = 10;
newvol(x);
return 0;
}
|
Java
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( "%" );
}
public static void main (String[] args)
{
double x = 10 ;
newvol(x);
}
}
|
Python3
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);
|
C#
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( "%" );
}
public static void Main ()
{
double x = 10;
newvol(x);
}
}
|
Javascript
<script>
function newvol( x)
{
document.write( "percentage increase "
+ "in the volume of the cube is "
+ (Math.pow(x, 3) / 10000 + 3 * x
+ (3 * Math.pow(x, 2)) / 100)
+ "%" );
}
let x = 10;
newvol(x);
</script>
|
Output: percentage increase in the volume of the cube is 33.1%
Time Complexity: O(1) because pow function will take constant time
Auxiliary Space: O(1), since no extra space has been taken.
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