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

main.py
import math

# Step 1: Find the radius of the cone and the radius of the circumscribed regular polygon
side_length = 6  # length of one side of the regular polygon
n = 8  # number of sides of the regular polygon
r = (side_length / 2) / math.sin(math.pi / n)  # radius of the circumscribed circle
cone_radius = r / math.sqrt(2)  # radius of the cone

# Step 2: Find the height of the cone
cone_height = math.sqrt(3) * cone_radius

# Step 3: Calculate the volume of the cone
cone_volume = (1 / 3) * math.pi * cone_radius ** 2 * cone_height

# Step 4: Calculate the volume of the regular polygon
polygon_volume = (n / 12) * cone_height * (3 * r ** 2 + cone_height ** 2) * math.tan(math.pi / n)

# Print the results
print("Cone volume:", cone_volume)
print("Regular polygon volume:", polygon_volume)
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