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

To find the volume of a regular polygon circumscribed around a cone, we need to determine the apothem (distance from center to a side) and perimeter of the polygon, as well as the height and base radius of the cone.

Here's some Go code to calculate the volume:

main.go
package main

import (
    "fmt"
    "math"
)

func main() {
    numSides := 8          // number of sides of the polygon
    radius := 5.0          // radius of the circumscribed circle
    height := 10.0         // height of the cone
    baseRadius := 3.0      // radius of the cone base
    s := math.Pi * radius   // perimeter of the polygon
    apothem := radius * math.Cos(math.Pi/float64(numSides)) // apothem of the polygon
    polygonArea := 0.5 * float64(numSides) * s * apothem     // area of the polygon
    coneVolume := (1.0/3.0) * math.Pi * math.Pow(baseRadius, 2) * height // volume of the cone
    totalVolume := polygonArea * height / 3.0 + coneVolume     // total volume
    fmt.Printf("Volume: %.2f\n", totalVolume)
}
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In this example, we have a regular octagon (8 sides) circumscribed around a cone with radius 5 and height 10, and a base radius of the cone is 3. The code calculates the perimeter (s) and apothem (apothem) of the polygon, and then uses these values to calculate the area (polygonArea). The volume of the cone is also calculated (coneVolume), and then the total volume (totalVolume) is determined by adding the volume of the tapered cylinder (polygon swept through the height of the cone) to the volume of the cone.

The output of this program should be:

main.go
Volume: 628.32
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