find the volume of a regular polygon circumscribed around a cone in ruby

main.rb
# define the number of sides of the polygon
num_sides = 8

# define the radius and height of the cone
radius = 5
height = 8

# calculate the slant height of the cone
slant_height = Math.sqrt(radius**2 + height**2)

# calculate the side length of the polygon
side_length = 2 * radius * Math.sin(Math::PI / num_sides)

# calculate the apothem of the polygon
apothem = radius * Math.cos(Math::PI / num_sides)

# calculate the perimeter of the polygon
perimeter = num_sides * side_length

# calculate the area of the polygon
area_polygon = 0.5 * perimeter * apothem

# calculate the volume of the cone circumscribed around the polygon
volume = (1.0 / 3.0) * Math::PI * radius**2 * height + num_sides * area_polygon * (slant_height / 3.0)

puts "The volume of the regular polygon circumscribed around the cone is #{volume.round(2)} cubic units."
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