find the volume of a regular polygon circumscribed around a cylinder in python

main.py
import math

def cylinder_circumradius_volume(n, r, h):
    # n is the number of sides of the regular polygon
    # r is the radius of the cylinder
    # h is the height of the cylinder
    
    # find the length of one side of the polygon
    s = 2 * r * math.sin(math.pi/n)
    
    # find the apothem of the polygon
    a = r * math.cos(math.pi/n)
    
    # find the perimeter of the polygon
    p = n * s
    
    # find the area of the base of the cylinder
    base_area = math.pi * r ** 2
    
    # find the area of the lateral surface of the cylinder
    lateral_area = p * h
    
    # find the total surface area of the cylinder
    total_area = lateral_area + 2 * base_area
    
    # find the volume of the cylinder
    volume = base_area * h
    
    # add the volume of the circumscribed polygon
    volume += (total_area * a) / 2
    
    return volume
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