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 <bits/stdc++.h>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 codeint 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 percentageimport 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 codepublic 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 percentagedef newvol(x): print("percentage increase in the" " volume of the sphere is " ,pow(x, 3) / 10000 + 3 * x + (3 * pow(x, 2)) / 100 ,"%")# Driver codex = 10.0newvol(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 percentageusing 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 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 sphere// if radius is increased by a given percentagefunction newvol(x){ document.write( "percentage increase in the" + " volume of the sphere is " +( Math.pow(x, 3) / 10000 + 3 * x + (3 * Math.pow(x, 2)) / 100) + "%");}// Driver codevar x = 10;newvol(x);// This code is contributed by 29AjayKumar </script> |
Output:
percentage increase in the volume of the sphere is 33.1%
Time Complexity: O(1)
Auxiliary Space: O(1) since using constant variables
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