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

To find the volume of a regular polygon circumscribed around a sphere, we need to first find the length of a side of the polygon, and then use that length to calculate the volume of the polygon.

Here's the Python code to accomplish this task:

main.py
import math

# Radius of the sphere
r = 5

# Number of sides of the regular polygon
n = 6

# Calculating the length of a side of the polygon using the radius of the sphere
s = 2 * r * math.sin(math.pi/n)

# Calculating the area of the polygon
a = (n * s**2)/(4 * math.tan(math.pi/n))

# Calculating the volume of the polygon by multiplying the area by the height h, which is equal to the diameter of the sphere
h = 2 * r
v = a * h

print("The volume of the regular polygon circumscribed around a sphere is:", v)
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In this code, we use the math module to perform mathematical calculations. We first input the radius of the sphere r, and the number of sides of the regular polygon n. Then we calculate s, which is the length of a side of the polygon using the formula s = 2 * r * sin(pi/n). We then use s to calculate the area of the polygon a using the formula a = (n * s^2) / (4 * tan(pi/n)). Finally, we calculate the volume of the polygon v by multiplying the area a by the height h, which is equal to the diameter of the sphere 2r. We then output the result using the print() function.