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

To find the volume of a regular polygon circumscribed around a cone in Python, we need to follow these steps:

  1. Find the radius of the cone and the radius of the circumscribed regular polygon.
  2. Find the height of the cone.
  3. Calculate the volume of the cone.
  4. Calculate the volume of the regular polygon using the formula V = (n/12) * h * (3r^2 + h^2) * tan(pi/n), where n is the number of sides, h is the height of the pyramid (same as the height of the cone), r is the radius of the circumscribed circle, and pi is the mathematical constant pi (3.141592...).

Here's the Python code to achieve this:

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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This will output the volume of the cone and the regular polygon circumscribed around it.

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