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

To find the volume of a regular polygon inscribed in a sphere, we can use the formula:

V = (2/3) * n * r^3 * sin(2*pi/n)

where:

• V is the volume of the regular polygon
• n is the number of sides of the regular polygon
• r is the radius of the sphere
• pi is the mathematical constant pi (3.14159...)
• sin() is the sine trigonometric function

Here's a Python function that calculates the volume of a regular polygon inscribed in a sphere:

main.py
import math

def volume_of_regular_polygon(n, r):
    pi = math.pi
    sin = math.sin(2*pi/n)
    V = (2/3) * n * r**3 * sin
    return V
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To use the function, simply call it with the number of sides and the radius of the sphere:

main.py
V = volume_of_regular_polygon(6, 5)
print(V)
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This will output the volume of a regular hexagon inscribed in a sphere with radius 5. You can change the values of n and r to calculate the volume of regular polygons of different sizes.