find the volume of a regular polygon circumscribed around a cylinder in rust

To find the volume of a regular polygon circumscribed around a cylinder, we can split the polygon into triangles and calculate the volume of each triangle using the formula for the volume of a pyramid. Then we can sum all the volumes to get the volume of the polygon.

Here's the Rust code to calculate the volume:

main.rs
use std::f64::consts::PI;

fn find_polygon_volume(num_sides: i32, radius: f64, height: f64) -> f64 {
    let apothem = radius;
    let slant_height = ((radius.powi(2) + height.powi(2)).sqrt()) * 2.0;
    let base_side_length = (2.0 * apothem * PI) / num_sides as f64;
    let triangle_height = (slant_height.powi(2) - base_side_length.powi(2) / 4.0).sqrt();
    let triangle_area = (base_side_length * triangle_height) / 2.0;
    let volume = (triangle_area * num_sides as f64 * height) / 3.0;
    volume
}

fn main() {
    let num_sides = 6;
    let radius = 5.0;
    let height = 10.0;
    let volume = find_polygon_volume(num_sides, radius, height);
    println!("Volume of regular polygon circumscribed around a cylinder is: {}", volume);
}
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In this code, num_sides represents the number of sides of the regular polygon, radius represents the radius of the cylinder, and height represents the height of the cylinder. We first find the apothem of the regular polygon, which is the distance from the center of a regular polygon to a side. We also find the slant_height of each triangular face of the regular polygon. Using the base side length, we calculate the triangle_height of each triangular face using the Pythagorean theorem. We use this triangle_height to calculate the triangle_area of each triangular face. Finally, we multiply triangle_area by the number of faces (i.e., num_sides) and height of the cylinder, and divide by 3 to get the volume.