find the volume of a regular polygon inscribed in a cone in ruby
To find the volume of a regular polygon inscribed in a cone, we can follow these steps:
Find the apothem of the polygon. This is the distance from the center of the polygon to the midpoint of one of its sides.
Find the slant height of the cone. This is the distance from the apex of the cone to any point on its base.
Find the height of the cone. This is the distance from the apex of the cone to the centroid of the polygon.
Use the formula for the volume of a pyramid to find the volume of the cone with the same base and height as the polygon.
Multiply the volume by the number of sides of the polygon.
Here's the code in Ruby:
main.rb
# Define the number of sides of the polygonnum_sides = 6# Define the radius and height of the coneradius = 5height = 10# Find the apothem of the polygonapothem = radius * Math.sin(Math::PI / num_sides)
# Find the slant height of the coneslant_height = Math.sqrt(radius**2 + height**2)
# Find the height of the conecentroid_height = (2/3.0) * apothem
# Find the volume of the conecone_volume = (1/3.0) * Math::PI * radius**2 * height
# Find the volume of the polygon inscribed in the conepolygon_volume = cone_volume * num_sides / 3.0puts "The volume of a regular polygon with #{num_sides} sides inscribed in a cone with radius #{radius} and height #{height} is #{polygon_volume}."