Example: Vault Height Calculator in C++

// Vault Height Calculator
#include <iostream>
#include <cmath>   // Required for sqrt()
#include <iomanip> // Required for setprecision() and fixed

using namespace std;

int main() {
    // Step 1: Declare variables for radius, width, half-width, and height
    double radius;
    double width;
    double halfWidth;
    double height;

    // Step 2: Prompt user for vault radius
    cout << "Enter the vault's radius (e.g., 6.0 meters): ";
    cin >> radius;

    // Step 3: Prompt user for vault width (span)
    cout << "Enter the vault's width (e.g., 10.0 meters): ";
    cin >> width;

    // Step 4: Calculate half-width
    halfWidth = width / 2.0;

    // Step 5: Validate inputs to prevent mathematical errors and illogical geometries
    if (radius <= 0 || width <= 0) {
        cout << "Error: Radius and width must be positive values." << endl;
        return 1; // Indicate an error
    }

    if (halfWidth > radius) {
        cout << "Error: The vault's half-width cannot be greater than its radius." << endl;
        cout << "This would imply an impossible or inverted circular segment." << endl;
        return 1; // Indicate an error
    }

    // Step 6: Calculate the vault height using the formula for a circular segment
    // Formula: h = R - sqrt(R^2 - (w/2)^2)
    // Where h is height, R is radius, w is width
    height = radius - sqrt(pow(radius, 2) - pow(halfWidth, 2));

    // Step 7: Display the calculated vault height
    cout << fixed << setprecision(4); // Format output to 4 decimal places
    cout << "\nCalculated Vault Height: " << height << " meters" << endl;

    return 0;
}