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Percentage increase in volume of the sphere if radius is increased by a given percentage
  • Last Updated : 05 Jul, 2019


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

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

C++

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// 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 code
int main()
{
    double x = 10;
    newvol(x);
    return 0;
}

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Java

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// Java program to find percentage increase
// in the volume of the sphere
// if radius 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 sphere is "
        +( Math.pow(x, 3) / 10000 + 3 * x
                + (3 * Math.pow(x, 2)) / 100)
        + "%");
}
  
// Driver code
public static void main (String[] args) 
{
        double x = 10;
    newvol(x);
}
}
  
// This code is contributed by anuj_67..

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Python3

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# Python3 program to find percentage increase
# in the volume of the sphere
# if radius is increased by a given percentage
  
def newvol(x):
  
    print("percentage increase in the"
        " volume of the sphere is "
        ,pow(x, 3) / 10000 + 3 * x
                + (3 * pow(x, 2)) / 100
            ,"%")
  
# Driver code
x = 10.0
newvol(x)
  
# This code is contributed mohit kumar 29

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C#

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// C# program to find percentage increase
// in the volume of the sphere
// if radius is increased by a given percentage
using 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 code
public static void Main () 
{
    double x = 10;
    newvol(x);
}
}
  
// This code is contributed by anuj_67..

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Output:

percentage increase in the volume of the sphere is 33.1%

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