find the surface area of a regular polygon inscribed in a cylinder in ruby

Here's a code snippet to find the surface area of a regular polygon inscribed in a cylinder in Ruby:

main.rb
# Function to calculate the surface area of a regular polygon inscribed in a cylinder
def polygonSurfaceArea(n, r, h)
    # n: number of sides of the polygon
    # r: radius of the cylinder
    # h: height of the cylinder

    # Calculate the side length of the polygon
    s = 2 * r * Math.sin(Math::PI / n)

    # Calculate the height of the polygon
    a = Math.sqrt(r**2 - (s / 2)**2)
    h_p = 2 * a

    # Calculate the surface area of the polygon
    sa_p = 0.5 * n * s * h_p

    # Calculate the surface area of the cylinder
    sa_c = 2 * Math::PI * r * h

    # Calculate the total surface area
    sa = sa_p + sa_c

    return sa
end

# Example usage
n = 6  # Hexagon
r = 5  # Radius of the cylinder
h = 10 # Height of the cylinder

sa = polygonSurfaceArea(n, r, h)
puts "Surface area of a regular polygon inscribed in a cylinder: #{sa}"
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In this code snippet, we define a function polygonSurfaceArea that calculates the surface area of a regular polygon inscribed in a cylinder. The function takes three parameters: n (number of sides of the polygon), r (radius of the cylinder), and h (height of the cylinder).

We first calculate the side length of the polygon using the formula s = 2 * r * sin(π/n), where π is the mathematical constant pi. We then calculate the height of the polygon using the Pythagorean theorem, and use that to calculate the surface area of the polygon.

Finally, we calculate the surface area of the cylinder (using the formula 2 * π * r * h) and add it to the surface area of the polygon to get the total surface area.

The code includes an example usage, where we calculate the surface area of a regular hexagon inscribed in a cylinder with radius 5 and height 10. The output should be:

Surface area of a regular polygon inscribed in a cylinder: 649.3636066021496