# 1. Introduction

The area of a circle is a fundamental concept in geometry that describes the size of the circle. The formula to calculate the area of a circle is A = Ï€r^2, where A is the area, Ï€ (pi) is a constant approximately equal to 3.14159, and r is the radius of the circle. This formula is derived from the properties of a circle and provides a way to calculate the area given the radius. This blog post will demonstrate how to write a Python program to calculate the area of a circle based on the radius provided by the user.

# 2. Program Steps

1. Prompt the user to enter the radius of the circle.

2. Use the formula A = Ï€r^2 to calculate the area. Use the math module to access the constant Ï€ (pi).

3. Display the calculated area to the user.

# 3. Code Program

``````# Step 1: Import the math module to access pi
import math

# Prompt the user to enter the radius of the circle
radius = float(input("Enter the radius of the circle: "))

# Step 2: Calculate the area using the formula A = Ï€r^2
area = math.pi * radius * radius

# Step 3: Display the area
print(f"The area of the circle with radius {radius} is: {area}")

``````

### Output:

```Enter the radius of the circle: 4
The area of the circle with radius 4.0 is: 50.26548245743669
```

### Explanation:

1. The program begins by importing the math module, which contains the constant Ï€ (pi), necessary for calculating the area of the circle.

2. It then prompts the user to enter the radius of the circle, which is read as a floating-point number to accommodate decimal values.

3. Using the area formula A = Ï€r^2, the program calculates the area. It multiplies Ï€ (accessed via math.pi) by the square of the radius.

4. Finally, the program prints the calculated area, providing the user with the area of the circle based on the provided radius. This demonstrates a practical application of mathematical formulas in programming to solve geometric problems.