Posted on by Kalkicode
Code Geometric

# Find volume of Hemisphere

A hemisphere is a three-dimensional shape that resembles half of a sphere. Calculating the volume of a hemisphere is a crucial task in various fields such as physics, engineering, and architecture, where hemispherical objects or structures are encountered. The volume of a hemisphere is used to determine the amount of space it occupies.

## Problem Statement

Given the radius (r) of the hemisphere, the task is to calculate its volume. The formula for finding the volume of a hemisphere in terms of its radius 'r' is:

Volume = (2/3) * π * r³

## Example Scenario

Imagine you are designing a water tank in the shape of a hemisphere for a fountain. You need to know the volume of water the tank can hold. Calculating the volume helps you determine the capacity of the tank, ensuring it meets the desired water storage requirement.

## Idea to Solve the Problem

To solve this problem, you can follow these steps:

1. Accept the radius 'r' of the hemisphere as an input.
2. Use the formula to calculate the volume of the hemisphere.
3. Display the calculated volume.

## Pseudocode

``````function hemisphere_volume(r):
volume = (2/3) * π * (r * r * r)
return volume

main:
r1 = 13
r2 = 4
r3 = 3.5

volume1 = hemisphere_volume(r1)
volume2 = hemisphere_volume(r2)
volume3 = hemisphere_volume(r3)

print("Hemisphere [ Radius :", r1, "]")
print("Volume :", volume1)

print("Hemisphere [ Radius :", r2, "]")
print("Volume :", volume2)

print("Hemisphere [ Radius :", r3, "]")
print("Volume :", volume3)``````

## Algorithm Explanation

1. Define a function `hemisphere_volume` that takes the radius 'r' as an input.
2. Inside the function, use the provided formula to calculate the volume of the hemisphere.
3. In the `main` function, set three test cases with different radii 'r'.
4. Calculate the volumes for each test case by calling the `hemisphere_volume` function.
5. Display the calculated volumes along with their respective radius values.

## Code Solution

``````/*
C Program
Find volume of Hemisphere
*/
#include <stdio.h>

#include <math.h>

//Calculate volume of hemisphere by radius
void hemisphere_volume(double r)
{
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
double volume = (2 * M_PI * (r * r * r)) / 3;
printf("\nVolume of hemisphere : %lf\n", volume);
}
int main()
{
//Simple Case
hemisphere_volume(13);
hemisphere_volume(4);
hemisphere_volume(3.5);
return 0;
}``````

#### Output

``````Given radius : 13.000000
Volume of hemisphere : 4601.386040

Volume of hemisphere : 134.041287

Volume of hemisphere : 89.797190``````
``````// Java Program
// Find volume of Hemisphere
class Hemisphere
{
//Calculate volume of hemisphere by radius
public void hemisphere_volume(double r)
{
System.out.print("\nGiven radius : " + r);
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
double volume = (2 * Math.PI * (r * r * r)) / 3;
System.out.print("\nVolume of of hemisphere : " + volume + "\n");
}
public static void main(String[] args)
{
Hemisphere obj = new Hemisphere();
//Simple Case
obj.hemisphere_volume(13);
obj.hemisphere_volume(4);
obj.hemisphere_volume(3.5);
}
}``````

#### Output

``````Given radius : 13.0
Volume of of hemisphere : 4601.386039957851

Volume of of hemisphere : 134.0412865531645

Volume of of hemisphere : 89.79719001510826``````
``````// C++ Program
// Find volume of Hemisphere
#include<iostream>
#include<math.h>
using namespace std;
class Hemisphere
{
public:
//Calculate volume of hemisphere by radius
void hemisphere_volume(double r)
{
cout << "\nGiven radius : " << r;
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
double volume = (2 * M_PI * (r * r * r)) / 3;
cout << "\nVolume of of hemisphere : " << volume << "\n";
}
};
int main()
{
Hemisphere obj ;
//Simple Case
obj.hemisphere_volume(13);
obj.hemisphere_volume(4);
obj.hemisphere_volume(3.5);
return 0;
}``````

#### Output

``````Given radius : 13
Volume of of hemisphere : 4601.39

Volume of of hemisphere : 134.041

Volume of of hemisphere : 89.7972``````
``````// C# Program
// Find volume of Hemisphere
using System;
class Hemisphere
{
//Calculate volume of hemisphere by radius
public void hemisphere_volume(double r)
{
Console.Write("\nGiven radius : " + r);
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
double volume = (2 * Math.PI * (r * r * r)) / 3;
Console.Write("\nVolume of of hemisphere : " + volume + "\n");
}
public static void Main(String[] args)
{
Hemisphere obj = new Hemisphere();
//Simple Case
obj.hemisphere_volume(13);
obj.hemisphere_volume(4);
obj.hemisphere_volume(3.5);
}
}``````

#### Output

``````Given radius : 13
Volume of of hemisphere : 4601.38603995785

Volume of of hemisphere : 134.041286553164

Volume of of hemisphere : 89.7971900151083``````
``````<?php
// Php Program
// Find volume of Hemisphere
class Hemisphere
{
//Calculate volume of hemisphere by radius
public  function hemisphere_volume(\$r)
{
echo "\nGiven radius : ". \$r;
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
\$volume = (2 * M_PI * (\$r * \$r * \$r)) / 3;
echo "\nVolume of of hemisphere : ". \$volume ."\n";
}
}

function main()
{
\$obj = new Hemisphere();
//Simple Case
\$obj->hemisphere_volume(13);
\$obj->hemisphere_volume(4);
\$obj->hemisphere_volume(3.5);
}
main();``````

#### Output

``````Given radius : 13
Volume of of hemisphere : 4601.3860399579

Volume of of hemisphere : 134.04128655316

Volume of of hemisphere : 89.797190015108``````
``````// Node Js Program
// Find volume of Hemisphere
class Hemisphere
{
//Calculate volume of hemisphere by radius
hemisphere_volume(r)
{
process.stdout.write("\nGiven radius : " + r);
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
var volume = (2 * Math.PI * (r * r * r)) / 3;
process.stdout.write("\nVolume of of hemisphere : " + volume + "\n");
}
}

function main()
{
var obj = new Hemisphere();
//Simple Case
obj.hemisphere_volume(13);
obj.hemisphere_volume(4);
obj.hemisphere_volume(3.5);
}
main();``````

#### Output

``````Given radius : 13
Volume of of hemisphere : 4601.386039957851

Volume of of hemisphere : 134.0412865531645

Volume of of hemisphere : 89.79719001510826``````
``````#  Python 3 Program
#  Find volume of Hemisphere
import math
class Hemisphere :
# Calculate volume of hemisphere by radius
def hemisphere_volume(self, r) :
print("\nGiven radius : ", r, end = "")
#  Formula of hemisphere volume
#    2πr³
#   -----
#     3
# Calculate volume of hemisphere
volume = (2 * math.pi * (r * r * r)) / 3
print("\nVolume of of hemisphere : ", volume ,"\n", end = "")

def main() :
obj = Hemisphere()
# Simple Case
obj.hemisphere_volume(13)
obj.hemisphere_volume(4)
obj.hemisphere_volume(3.5)

if __name__ == "__main__": main()``````

#### Output

``````Given radius :  13
Volume of of hemisphere :  4601.386039957851

Volume of of hemisphere :  134.0412865531645

Volume of of hemisphere :  89.79719001510826``````
``````#  Ruby Program
#  Find volume of Hemisphere
class Hemisphere

# Calculate volume of hemisphere by radius
def hemisphere_volume(r)

#  Formula of hemisphere volume
#    2πr³
#   -----
#     3
# Calculate volume of hemisphere
volume = (2 * Math::PI * (r * r * r)) / 3
print("\nVolume of of hemisphere : ", volume ,"\n")
end
end
def main()

obj = Hemisphere.new()
# Simple Case
obj.hemisphere_volume(13)
obj.hemisphere_volume(4)
obj.hemisphere_volume(3.5)
end
main()``````

#### Output

``````Given radius : 13
Volume of of hemisphere : 4601.386039957851

Volume of of hemisphere : 134.0412865531645

Volume of of hemisphere : 89.79719001510826
``````
``````// Scala Program
// Find volume of Hemisphere
class Hemisphere
{
//Calculate volume of hemisphere by radius
def hemisphere_volume(r: Double): Unit = {
print("\nGiven radius : " + r);
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
var volume: Double = (2 * Math.PI * (r * r * r)) / 3;
print("\nVolume of of hemisphere : " + volume + "\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: Hemisphere = new Hemisphere();
//Simple Case
obj.hemisphere_volume(13);
obj.hemisphere_volume(4);
obj.hemisphere_volume(3.5);
}
}``````

#### Output

``````Given radius : 13.0
Volume of of hemisphere : 4601.386039957851

Volume of of hemisphere : 134.0412865531645

Volume of of hemisphere : 89.79719001510826``````
``````// Swift Program
// Find volume of Hemisphere
import Foundation
class Hemisphere
{
//Calculate volume of hemisphere by radius
func hemisphere_volume(_ r: Double)
{
print("\nGiven radius : ", r, terminator: "");
// Formula of hemisphere volume
//   2πr³
//  -----
//    3
//Calculate volume of hemisphere
let volume: Double = (2 * Double.pi * (r * r * r)) / 3;
print("\nVolume of of hemisphere : ", volume ,"\n", terminator: "");
}
}
func main()
{
let obj: Hemisphere = Hemisphere();
//Simple Case
obj.hemisphere_volume(13);
obj.hemisphere_volume(4);
obj.hemisphere_volume(3.5);
}
main();``````

#### Output

``````Given radius :  13.0
Volume of of hemisphere :  4601.38603995785

Volume of of hemisphere :  134.041286553164

Volume of of hemisphere :  89.7971900151083``````

## Output Explanation

The code calculates the volume for each test case and displays the results. For a hemisphere with a radius 'r' = 13, the volume is approximately 4601.386040. Similarly, for radii 'r' = 4 and 'r' = 3.5, the volumes are approximately 134.041287 and 89.797190, respectively.

## Time Complexity

The time complexity of this code is constant O(1) because the calculations involve basic arithmetic operations (multiplication and division) and the use of the mathematical constant π (pi). These operations are computed in constant time regardless of the input size. The program performs a fixed number of operations for each test case, making it efficient.

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