Percentage increase in volume of the sphere if radius is increased by a given percentage
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*Ï€a^3
- new radius after increase = a + ax/100
- so, new volume = 4/3*Ï€(a^3 + (ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)
- change in volume = 4/3*Ï€((ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)
- percentage increase in volume = (4/3*Ï€*((ax/100)^3 + 3a^3x/100 + 3a^3x^2/10000)/4/3*Ï€*a^3) * 100 = x^3/10000 + 3x + 3x^2/100
C++
#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;
}
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 sphere is "
+( Math.pow(x, 3 ) / 10000 + 3 * x
+ ( 3 * Math.pow(x, 2 )) / 100 )
+ "%" );
}
public static void main (String[] args)
{
double x = 10 ;
newvol(x);
}
}
|
Python3
def newvol(x):
print ( "percentage increase in the"
" volume of the sphere is "
, pow (x, 3 ) / 10000 + 3 * x
+ ( 3 * pow (x, 2 )) / 100
, "%" )
x = 10.0
newvol(x)
|
C#
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)
+ "%" );
}
public static void Main ()
{
double x = 10;
newvol(x);
}
}
|
Javascript
<script>
function 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)
+ "%" );
}
var x = 10;
newvol(x);
</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
Last Updated :
09 Sep, 2022
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