# Python Program to Find the Area and Perimeter of the Circle

Problem Description

Write a Python Program to find the area and perimeter of the circle.

What is Area of circle?

Area of circle is defined as pi*r*r where pi is a constant whose value is (22/7 or 3.142) and r is the radius of a circle.

Formula to calculate the area of circle is: Area = pi*r*r

Example:
If the radius of a circle is 5, then area of circle is pi*r*r = 3.14*5*5 = 78.5.

What is the perimeter of a circle?

The perimeter of a circle is also known as the circumference. It refers to the total length of the boundary or the distance around the circle.

Formula to calculate the area of Perimeter = 2 * π * radius

Example:
If the radius of a circle is 5, then area of circle is 2 * π * radius = 2*3.14*5 = 31.4

Here are the methods for finding the Area of a Circle and perimeter using Python.

Method 1: Area of Circle and perimeter using Math Module

In this approach, we calculate the area of a circle and perimeter using the math module.

Program/Source Code

Here is the source code of the Python Program to take the radius from the user and find the area of the circle using math module. The program output is also shown below.

```import math

# Calculate the area of the circle
area = math.pi * radius ** 2

# Calculate the perimeter of the circle
perimeter = 2 * math.pi * radius

print("Area of the circle:", area)
print("Perimeter of the circle:", perimeter)```
Program Explanation

1. In this program, we first prompt the user to enter the radius of the circle.
2. Then, using the formula area = pi * radius2, we calculate the area of the circle.
3. Next, using the formula perimeter = 2 * pi * radius, we calculate the perimeter of the circle.
4. Finally, we display the calculated area and perimeter.

Time Complexity: O(1)
The time complexity of the program is O(1) as the calculations are performed in constant time regardless of the input size.

Space Complexity: O(1)
The space complexity is also O(1) as the program uses a fixed amount of memory to store the variables and the math module.

Runtime Test Cases

Testcase 1: Here, the given radius is “5”

```Enter the radius of the circle: 5
Area of circle: 78.54
Perimeter of circle: 31.42```

Testcase 2: Here, the given radius is “10”

```Enter the radius of the circle: 10
Area of the circle: 314.16
Perimeter of the circle: 62.83```

Method 2: Finds the area of the circle using classes

The program takes the radius from the user and finds the area of the circle using classes.

Program/Source Code

Here is the source code of the Python Program to take the radius from the user and find the area of the circle using classes. The program output is also shown below.

```import math
class circle():
def area(self):
def perimeter(self):

obj=circle(r)
print("Area of circle:",round(obj.area(),2))
print("Perimeter of circle:",round(obj.perimeter(),2))```
Program Explanation

1. User must enter the value of radius.
2. A class called circle is created and the __init__() method is used to initialize values of that class.
3. A method called as area returns math.pi*(self.radius**2) which is the area of the class.
3. Another method called perimeter returns 2*math.pi*self.radius which is the perimeter of the class.
5. An object for the class is created.
6. Using the object, the methods area() and perimeter() are called.
7. The area and perimeter of the circle is printed.

Time Complexity: O(1)
The time complexity of the program is O(1) as the calculations are performed in constant time regardless of the input size.

Space Complexity: O(1)
The space complexity is also O(1) as the program uses a fixed amount of memory to store the variables and the math module, and the space required does not depend on the input size.

Runtime Test Cases

Testcase 1: Here, the given radius is “5”

```Enter radius of circle: 5
Area of circle: 78.54
Perimeter of circle: 31.42```

Testcase 2: Here, the given radius is “10”

```Enter radius of circle: 10
Area of circle: 314.16
Perimeter of circle: 62.83```

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