C++ Program to Find the Area of a Circular Ring

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Introduction

A circular ring is a geometric figure that consists of the area between two concentric circles. This shape is commonly encountered in engineering, architecture, and design. rc Calculating the area of a circular ring is a straightforward task that requires the radii of the inner and outer circles.

In this article, we will explore the concept of a circular ring, the mathematical formula for its area, and its implementation in C++ with a detailed explanation and output example.

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Formula

The area of a circular ring can be calculated by subtracting the area of the inner circle from the area of the outer circle. The formula is as follows:

• Area of a Circle: A = π × r², where r is the radius of the circle.
• Area of a Circular Ring: A = π × (R² - r²), where:
  • R is the radius of the outer circle.
  • r is the radius of the inner circle.

Here, π (pi) is approximately 3.14159. The difference between the areas of the two circles gives the area of the ring.

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Code

Here is the C++ program to compute the area of a circular ring:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    // Variables for inner and outer radii
    double innerRadius, outerRadius;

    // Input the radii
    cout << "Enter the radius of the inner circle: ";
    cin >> innerRadius;
    cout << "Enter the radius of the outer circle: ";
    cin >> outerRadius;

    // Check if outer radius is greater than inner radius
    if (outerRadius <= innerRadius) {
        cout << "Error: Outer radius must be greater than inner radius." << endl;
        return 1; // Exit the program
    }

    // Calculate the area of the circular ring
    double ringArea = M_PI * (pow(outerRadius, 2) - pow(innerRadius, 2));

    // Display the result
    cout << "The area of the circular ring is: " << ringArea << endl;

    return 0;
}

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Output

When the program is executed, it prompts the user to enter the radii of the inner and outer circles. Below is an example of the program in action:

Enter the radius of the inner circle: 3
Enter the radius of the outer circle: 5
The area of the circular ring is: 50.2655

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Explanation

Let us break down the steps in the program:

• Input: The program asks the user to input two radii:
  • The radius of the inner circle (innerRadius).
  • The radius of the outer circle (outerRadius).
  It validates that the outer radius is greater than the inner radius. If not, an error message is displayed.
• Area Calculation: Using the formula A = π × (R² - r²), the program calculates the area of the circular ring. The pow function from the cmath library is used to square the radii.
• Output: The calculated area is displayed to the user in a formatted manner. The value of π is provided by M_PI, a constant defined in the cmath library.

This program is efficient and demonstrates a practical way of solving problems involving geometric calculations using C++.