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

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

  1. Determine the number of sides of the regular polygon.
  2. Calculate the length of each side of the polygon.
  3. Calculate the slant height of the cone.
  4. Calculate the height of the cone.
  5. Calculate the area of the base of the polygon.
  6. Calculate the volume of the polygon.

Here is the Swift code to accomplish this:

main.swift
func volumeOfRegularPolygonInCone(n: Int, r: Float, h: Float) -> Float {
    let π: Float = .pi

    // Step 1 - Determine the number of sides of the regular polygon
    let sides = Float(n)

    // Step 2 - Calculate the length of each side of the polygon
    let a = 2 * r * sin(π / sides)

    // Step 3 - Calculate the slant height of the cone
    let slantHeight = sqrt(pow(r, 2) + pow(h, 2))

    // Step 4 - Calculate the height of the cone
    let height = h

    // Step 5 - Calculate the area of the base of the polygon
    let baseArea = (sides * pow(a, 2)) / (4 * tan(π / sides))

    // Step 6 - Calculate the volume of the polygon
    let volume = (1 / 3) * baseArea * height

    return volume
}
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To use this function, call it with the number of sides of the regular polygon, the radius of the cone, and the height of the cone:

main.swift
let volume = volumeOfRegularPolygonInCone(n: 6, r: 2.0, h: 5.0)
print("The volume is: \(volume)")
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