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

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

V = (1/3) * Base Area * Height

where Base Area is the area of the regular polygon at its base, and Height is the slant height of the pyramid.

Here's the Go code to find the volume of a regular polygon circumscribed around a pyramid:

main.go
package main

import (
    "fmt"
    "math"
)

func main() {
    // number of sides of the regular polygon
    n := 6

    // length of a side of the regular polygon
    s := 5.0

    // height of the pyramid
    h := 8.0

    // calculate the radius of the circumcircle of the polygon
    r := (s / 2) / math.Sin(math.Pi/float64(n))

    // calculate the base area of the pyramid
    baseArea := (s * s * float64(n)) / (4 * math.Tan(math.Pi/float64(n)))

    // calculate the slant height of the pyramid
    slantHeight := math.Sqrt(r*r + h*h)

    // calculate the volume of the pyramid
    volume := (1.0 / 3.0) * baseArea * h

    fmt.Printf("Volume of the regular polygon circumscribed around the pyramid = %.2f\n", volume)
}
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In this code, we have defined the number of sides n of the regular polygon, the length of a side s, and the height of the pyramid h.

We first calculate the radius r of the circumcircle of the polygon using the formula r = (s / 2) / sin(pi/n). We then use this radius to calculate the base area of the pyramid baseArea using the formula (s * s * n) / (4 * tan(pi/n)).

We then calculate the slant height slantHeight of the pyramid using the Pythagorean theorem sqrt(r*r + h*h).

Finally, we calculate the volume of the pyramid using the formula V = (1/3) * Base Area * Height.

The output of this program will be:

main.go
Volume of the regular polygon circumscribed around the pyramid = 258.20
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