Find the surface area of sphere
In geometry, a sphere is a three-dimensional object that is perfectly round, with all points on its surface equidistant from its center. The surface area of a sphere refers to the total area covered by its outer surface.
Problem Statement
Given the radius of a sphere, the task is to calculate its surface area. The formula for finding the surface area of a sphere in terms of its radius 'r' is:
Surface Area = 4 * π * r^2
Example Scenario
Imagine you are an astrophysicist studying planets and celestial bodies. You need to determine the surface area of a planet to understand its heat exchange with space. By calculating the surface area of the planet (approximated as a sphere) using its radius, you can better comprehend its thermal characteristics.
Idea to Solve the Problem
To solve this problem, we can follow these steps:
- Accept the radius of the sphere as input.
- Use the formula to calculate the surface area of the sphere.
- Display the calculated surface area.
Pseudocode
function sphere_area(radius):
area = 4 * π * radius^2
return area
main:
radius1 = 3
radius2 = 7
radius3 = 5.8
area1 = sphere_area(radius1)
area2 = sphere_area(radius2)
area3 = sphere_area(radius3)
print("Sphere Surface [ radius :", radius1, "]")
print("Surface Area :", area1)
print("Sphere Surface [ radius :", radius2, "]")
print("Surface Area :", area2)
print("Sphere Surface [ radius :", radius3, "]")
print("Surface Area :", area3)
Algorithm Explanation
- Define a function
sphere_area
that takes the radius as input. - Inside the function, use the provided formula to calculate the surface area of the sphere.
- In the
main
function, set three test cases with different radii: 3, 7, and 5.8. - Calculate the surface areas for each test case by calling the
sphere_area
function. - Display the calculated surface areas along with their respective radii.
Code Solution
//C Program
//Find the surface area of sphere
#include <stdio.h>
#include <math.h>
//Calculate surface area of sphere by given radius
void sphere_area(double radius)
{
// Formula
// 4πr²
double area = 4 * M_PI * (radius * radius);
//Display result
printf(" Sphere Surface [ radius : %lf] ", radius);
printf("\n Surface Area : %lf\n\n", area);
}
int main()
{
//Test Case
sphere_area(3);
sphere_area(7);
sphere_area(5.8);
return 0;
}
Output
Sphere Surface [ radius : 3.000000]
Surface Area : 113.097336
Sphere Surface [ radius : 7.000000]
Surface Area : 615.752160
Sphere Surface [ radius : 5.800000]
Surface Area : 422.732707
// Java Program
// Find the surface area of sphere
class Sphere
{
//Calculate surface area of sphere by given radius
public void sphere_area(double radius)
{
// Formula
// 4πr²
double area = 4 * Math.PI * (radius * radius);
//Display result
System.out.print(" Sphere Surface [ radius : " + radius + "] ");
System.out.print("\n Surface Area : " + area + "\n\n");
}
public static void main(String[] args)
{
Sphere obj = new Sphere();
//Test Case
obj.sphere_area(3);
obj.sphere_area(7);
obj.sphere_area(5.8);
}
}
Output
Sphere Surface [ radius : 3.0]
Surface Area : 113.09733552923255
Sphere Surface [ radius : 7.0]
Surface Area : 615.7521601035994
Sphere Surface [ radius : 5.8]
Surface Area : 422.7327074670426
// C++ Program
// Find the surface area of sphere
#include<iostream>
#include <math.h>
using namespace std;
class Sphere
{
public:
//Calculate surface area of sphere by given radius
void sphere_area(double radius)
{
// Formula
// 4πr²
double area = 4 *M_PI *(radius *radius);
cout << " Sphere Surface [ radius : " << radius << "] ";
cout << "\n Surface Area : " << area << "\n\n";
}
};
int main()
{
Sphere obj = Sphere();
//Test Case
obj.sphere_area(3);
obj.sphere_area(7);
obj.sphere_area(5.8);
return 0;
}
Output
Sphere Surface [ radius : 3]
Surface Area : 113.097
Sphere Surface [ radius : 7]
Surface Area : 615.752
Sphere Surface [ radius : 5.8]
Surface Area : 422.733
<?php
// Php Program
// Find the surface area of sphere
class Sphere
{
//Calculate surface area of sphere by given radius
public function sphere_area($radius)
{
// Formula
// 4πr²
$area = 4 * M_PI *($radius *$radius);
//Display result
echo(" Sphere Surface [ radius : ". $radius ."] ");
echo("\n Surface Area : ". $area ."\n\n");
}
}
function main()
{
$obj = new Sphere();
//Test Case
$obj->sphere_area(3);
$obj->sphere_area(7);
$obj->sphere_area(5.8);
}
main();
Output
Sphere Surface [ radius : 3]
Surface Area : 113.09733552923
Sphere Surface [ radius : 7]
Surface Area : 615.7521601036
Sphere Surface [ radius : 5.8]
Surface Area : 422.73270746704
// C# Program
// Find the surface area of sphere
using System;
class Sphere
{
//Calculate surface area of sphere by given radius
public void sphere_area(double radius)
{
// Formula
// 4πr²
double area = 4 * Math.PI * (radius * radius);
Console.Write(" Sphere Surface [ radius : " + radius + "] ");
Console.Write("\n Surface Area : " + area + "\n\n");
}
public static void Main(String[] args)
{
Sphere obj = new Sphere();
//Test Case
obj.sphere_area(3);
obj.sphere_area(7);
obj.sphere_area(5.8);
}
}
Output
Sphere Surface [ radius : 3]
Surface Area : 113.097335529233
Sphere Surface [ radius : 7]
Surface Area : 615.752160103599
Sphere Surface [ radius : 5.8]
Surface Area : 422.732707467043
// Node Js Program
// Find the surface area of sphere
class Sphere
{
//Calculate surface area of sphere by given radius
sphere_area(radius)
{
// Formula
// 4πr²
var area = 4 * Math.PI * (radius *radius);
//Display result
process.stdout.write(" Sphere Surface [ radius : " + radius + "] ");
process.stdout.write("\n Surface Area : " + area + "\n\n");
}
}
function main(args)
{
var obj = new Sphere();
//Test Case
obj.sphere_area(3);
obj.sphere_area(7);
obj.sphere_area(5.8);
}
main();
Output
Sphere Surface [ radius : 3]
Surface Area : 113.09733552923255
Sphere Surface [ radius : 7]
Surface Area : 615.7521601035994
Sphere Surface [ radius : 5.8]
Surface Area : 422.7327074670426
# Python 3 Program
# Find the surface area of sphere
import math
class Sphere :
# Calculate surface area of sphere by given radius
def sphere_area(self, radius) :
# Formula
# 4πr²
area = 4 * math.pi * (radius * radius)
# Display result
print(" Sphere Surface [ radius : ", radius ,"] ", end = "")
print("\n Surface Area : ", area ,"\n\n", end = "")
def main() :
obj = Sphere()
# Test Case
obj.sphere_area(3)
obj.sphere_area(7)
obj.sphere_area(5.8)
if __name__ == "__main__": main()
Output
Sphere Surface [ radius : 3 ]
Surface Area : 113.09733552923255
Sphere Surface [ radius : 7 ]
Surface Area : 615.7521601035994
Sphere Surface [ radius : 5.8 ]
Surface Area : 422.7327074670426
# Ruby Program
# Find the surface area of sphere
class Sphere
# Calculate surface area of sphere by given radius
def sphere_area(radius)
# Formula
# 4πr²
area = 4 * Math::PI * (radius * radius)
# Display result
print(" Sphere Surface [ radius : ", radius ,"] ")
print("\n Surface Area : ", area ,"\n\n")
end
end
def main()
obj = Sphere.new()
# Test Case
obj.sphere_area(3)
obj.sphere_area(7)
obj.sphere_area(5.8)
end
main()
Output
Sphere Surface [ radius : 3]
Surface Area : 113.09733552923255
Sphere Surface [ radius : 7]
Surface Area : 615.7521601035994
Sphere Surface [ radius : 5.8]
Surface Area : 422.7327074670426
// Scala Program
// Find the surface area of sphere
class Sphere
{
//Calculate surface area of sphere by given radius
def sphere_area(radius: Double): Unit = {
// Formula
// 4πr²
var area: Double = 4 * Math.PI * (radius * radius);
//Display result
print(" Sphere Surface [ radius : " + radius + "] ");
print("\n Surface Area : " + area + "\n\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: Sphere = new Sphere();
//Test Case
obj.sphere_area(3);
obj.sphere_area(7);
obj.sphere_area(5.8);
}
}
Output
Sphere Surface [ radius : 3.0]
Surface Area : 113.09733552923255
Sphere Surface [ radius : 7.0]
Surface Area : 615.7521601035994
Sphere Surface [ radius : 5.8]
Surface Area : 422.7327074670426
// Swift Program
// Find the surface area of sphere
class Sphere
{
//Calculate surface area of sphere by given radius
func sphere_area(_ radius: Double)
{
// Formula
// 4πr²
let area: Double = 4 * Double.pi * (radius * radius);
//Display result
print(" Sphere Surface [ radius : ", radius ,"] ", terminator: "");
print("\n Surface Area : ", area ,"\n\n", terminator: "");
}
}
func main()
{
let obj: Sphere = Sphere();
//Test Case
obj.sphere_area(3);
obj.sphere_area(7);
obj.sphere_area(5.8);
}
main();
Output
Sphere Surface [ radius : 3.0 ]
Surface Area : 113.097335529233
Sphere Surface [ radius : 7.0 ]
Surface Area : 615.752160103599
Sphere Surface [ radius : 5.8 ]
Surface Area : 422.732707467043
Output Explanation
The code calculates the surface area for each test case and displays the results. For a sphere with a radius of 3, the surface area is approximately 113.097336. Similarly, for radii of 7 and 5.8, the surface areas are approximately 615.752160 and 422.732707, respectively.
Time Complexity
The time complexity of this code is constant O(1) because the calculations involve basic arithmetic operations, which take a constant amount of 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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