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

To find the volume of a regular polygon circumscribed around a sphere, we can use the following formula:

V = (4/3) * π * r^3

where r is the radius of the sphere.

Let's assume we have a regular polygon with n sides and a circumscribed sphere of radius r. We can calculate the length of each side of the polygon using trigonometry:

a = 2 * r * sin(π/n)

Once we have the length of each side, we can calculate the area of the polygon using the following formula:

A = (n * a^2) / (4 * tan(π/n))

Finally, we can calculate the volume of the circumscribed sphere using the previously mentioned formula:

V = (4/3) * π * r^3

Putting it all together, we get the following Go code to find the volume of a regular polygon circumscribed around a sphere:

main.go
package main

import (
    "fmt"
    "math"
)

func main() {
    n := 6      // number of polygon sides
    r := 4.0    // radius of circumscribed sphere

    a := 2 * r * math.Sin(math.Pi/float64(n))

    A := (float64(n) * math.Pow(a, 2)) / (4 * math.Tan(math.Pi/float64(n)))

    V := (4.0/3.0) * math.Pi * math.Pow(r, 3)

    fmt.Printf("Volume of regular polygon circumscribed around a sphere: %f\n", V)
}
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