find the volume of a regular polygon inscribed in a cone in go

To find the volume of a regular polygon inscribed in a cone, we need to follow a few steps:

1. Find the slant height (l) of the cone
2. Find the apothem (a) of the regular polygon
3. Find the area of the regular polygon (A)
4. Use the formula V = (1/3) * A * l to find the volume (V) of the cone

Here's the implementation in Go:

main.go
package main

import (
    "fmt"
    "math"
)

func main() {
    // input parameters
    r := 3.0 // radius of the base of the cone
    n := 6   // number of sides of the regular polygon

    slantHeight := math.Sqrt((r * r) + (apothem(n, r) * apothem(n, r)))
    area := (float64(n) / 2) * apothem(n, r) * sideLength(n, r)
    volume := (1.0 / 3) * area * slantHeight

    fmt.Printf("Volume of the cone: %.2f", volume)
}

func apothem(n int, r float64) float64 {
    return r * math.Cos(math.Pi/float64(n))
}

func sideLength(n int, r float64) float64 {
    return 2 * r * math.Sin(math.Pi/float64(n))
}
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In this implementation, r is the radius of the base of the cone, and n is the number of sides of the regular polygon inscribed in the cone. We first calculate the slant height of the cone using the Pythagorean theorem. Then, we calculate the area of the regular polygon using the apothem and side length formulas. Finally, we use the formula for the volume of a cone to find the volume of the cone.

Note: This implementation assumes that the cone is a right circular cone with the center of its base at the vertex of the cone. If the cone is not a right circular cone, this implementation may not be accurate.