find the volume of a regular polygon inscribed in a cylinder in ruby

To find the volume of a regular polygon inscribed in a cylinder, we need to first find the area of the base of the cylinder and the side length of the polygon. Then, we can use the formula for the volume of a regular polygon to calculate the volume of the polygon, and add it to the volume of the cylinder.

Here is the implementation in Ruby:

main.rb
def volume_regular_polygon_inscribed_in_cylinder(radius, height, num_sides)
  base_area = Math::PI * radius ** 2
  side_length = 2 * radius * Math.sin(Math::PI / num_sides)
  polygon_area = (num_sides * side_length ** 2) / (4 * Math.tan(Math::PI / num_sides))
  cylinder_volume = base_area * height
  polygon_volume = polygon_area * height
  total_volume = cylinder_volume + polygon_volume
  return total_volume
end
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The volume_regular_polygon_inscribed_in_cylinder function takes in the radius and height of the cylinder, as well as the num_sides of the inscribed polygon. It first calculates the area of the base of the cylinder using the formula for the area of a circle. Then, it calculates the side length of the inscribed polygon using the formula for the apothem of a regular polygon. Using this side length, it calculates the area of the polygon using the formula for the area of a regular polygon. Finally, it calculates the volumes of both the cylinder and the polygon, and adds them together to get the total volume.

Example usage:

main.rb
volume = volume_regular_polygon_inscribed_in_cylinder(5, 10, 6)
puts "The volume of the inscribed polygon and cylinder is #{volume} cubic units."
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Output:

main.rb
The volume of the inscribed polygon and cylinder is 1227.5377466117307 cubic units.
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