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Given that the radius of a hemisphere is changed by a fixed percentage so, the target is to calculate the percentage changed in the volume of the hemisphere.
Examples:
Input: r = 20%
Output: 72.80%
Input: r = 70%
Output: 391.30 %
Approach:
- Let, the radius of the hemisphere =
- Given percentage increase =
- Volume before increase =
- New radius after increase =
- So, new volume =
- Change in volume =
- Percentage increase in volume
Below is the implementation of the above approach:
CPP
#include <iostream>
#include <math.h>
using namespace std;
void new_vol(double x)
{
if (x > 0) {
cout << "% change in the "
<< "volume of the hemisphere: "
<< pow(x, 3) / 10000 + 3 * x
+ (3 * pow(x, 2)) / 100
<< "%"
<< " increase\n";
}
else if (x < 0) {
cout << "% change in the "
<< "volume of the hemisphere: "
<< pow(x, 3) / 10000 + 3 * x
+ (3 * pow(x, 2)) / 100
<< "% decrease\n";
}
else {
cout << "Volume remains the same.";
}
}
int main()
{
double x = -10.0;
new_vol(x);
return 0;
}
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Java
class GFG
{
static void new_vol(double x)
{
if (x > 0)
{
System.out.print("% change in the "
+ "volume of the hemisphere: "
+ (Math.pow(x, 3) / 10000 + 3 * x
+ (3 * Math.pow(x, 2)) / 100)
+ "%"
+ " increase\n");
}
else if (x < 0)
{
System.out.print("% change in the "
+ "volume of the hemisphere: "
+ (Math.pow(x, 3) / 10000 + 3 * x
+ (3 * Math.pow(x, 2)) / 100)
+ "% decrease\n");
}
else
{
System.out.print("Volume remains the same.");
}
}
public static void main(String[] args)
{
double x = -10.0;
new_vol(x);
}
}
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Python
def new_vol(x):
if (x > 0):
print("% change in the volume of the hemisphere: ", pow(x, 3) / 10000 + 3 * x + (3 * pow(x, 2)) / 100,"% increase")
elif (x < 0):
print("% change in the volume of the hemisphere: ", pow(x, 3) / 10000 + 3 * x + (3 * pow(x, 2)) / 100,"% decrease")
else:
print("Volume remains the same.")
x = -10.0
new_vol(x)
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C#
using System;
class GFG
{
static void new_vol(double x)
{
if (x > 0)
{
Console.Write("% change in the "
+ "volume of the hemisphere: "
+ (Math.Pow(x, 3) / 10000 + 3 * x
+ (3 * Math.Pow(x, 2)) / 100)
+ "%"
+ " increase\n");
}
else if (x < 0)
{
Console.Write("% change in the "
+ "volume of the hemisphere: "
+ (Math.Pow(x, 3) / 10000 + 3 * x
+ (3 * Math.Pow(x, 2)) / 100)
+ "% decrease\n");
}
else
{
Console.Write("Volume remains the same.");
}
}
public static void Main()
{
double x = -10.0;
new_vol(x);
}
}
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Javascript
function new_vol(x)
{
if (x > 0)
{
document.write("% change in the "
+ "volume of the hemisphere: "
+ (Math.pow(x, 3) / 10000 + 3 * x
+ (3 * Math.pow(x, 2)) / 100)
+ "%"
+ " increase\n");
}
else if (x < 0)
{
document.write("% change in the "
+ "volume of the hemisphere: "
+ (Math.pow(x, 3) / 10000 + 3 * x
+ (3 * Math.pow(x, 2)) / 100)
+ "% decrease\n");
}
else
{
document.write("Volume remains the same.");
}
}
var x = -10.0;
new_vol(x);
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Output: % change in the volume of the hemisphere: -27.1% decrease
Time Complexity: O(1)
Auxiliary Space: O(1) as using only constant variables
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