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++
// 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 codeint 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 percentageimport 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 codepublic 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 percentagedef 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 percentageusing 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 codepublic static void Main (){ double x = 10; newvol(x);}}// This code is contributed by anuj_67.. |
Javascript
<script>// javascript program to find percentage increase// in the volume of the cube// if a side of cube is increased// by a given percentagefunction 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) + "%" );}// Driver code let x = 10; newvol(x); // This code is contributed by gauravrajput1 </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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