find the volume of a regular polygon inscribed in a cylinder in python

To find the volume of a regular polygon inscribed in a cylinder, we need to know the radius of the cylinder and the number of sides of the polygon. We can use the formula for the area of a regular polygon to determine the area of its base, which is a regular polygon, and then multiply it by the height of the cylinder to get the volume.

Below is a Python function that takes in the radius and number of sides of the inscribed polygon as arguments and returns the volume of the cylinder:

main.py
import math

def volume_of_polygon_in_cylinder(radius, sides, height):
    apothem = radius * math.cos(math.pi / sides)
    side_length = 2 * radius * math.sin(math.pi / sides)
    base_area = (sides * side_length * apothem) / 2
    volume = base_area * height
    return volume
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Here, we first calculate the apothem and side length of the polygon using the given radius and number of sides. Then, we calculate the area of the base of the cylinder by multiplying the area of the regular polygon with the number of sides with its apothem/2, and finally, we multiply the area of the base with the height of the cylinder to get the volume of the polygon inside the cylinder.

We can call this function with different inputs to find the volume of regular polygons inscribed in various cylinders.