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

To find the volume of a regular polygon that is circumscribed around a cone, we need to follow the steps below:

1. Calculate the slant height of the cone, which is the distance between the vertex of the cone and the point where the base of the cone intersects with the circumscribed polygon.
2. Calculate the apothem of the polygon, which is the distance between the center of the polygon and the midpoint of one of its sides.
3. Calculate the perimeter of the polygon, which is the sum of the lengths of all its sides.
4. Calculate the area of the polygon, which is half the product of its apothem and perimeter.
5. Calculate the volume of the circumscribed polygon by multiplying the area of the polygon by the height of the cone.

The Rust code to implement the above steps is as follows:

main.rs
fn main() {
    let radius = 5.0; // radius of the base of the cone
    let height = 10.0; // height of the cone
    let num_sides = 6; // number of sides in the circumscribed polygon

    let slant_height = f64::sqrt(radius.powi(2) + height.powi(2)); // calculate slant height
    let apothem = radius/(2.0*f64::tan(std::f64::consts::PI/(num_sides as f64))); // calculate apothem
    let perimeter = 2.0*radius*f64::sin(std::f64::consts::PI/(num_sides as f64))*num_sides as f64; // calculate perimeter
    let area = 0.5*apothem*perimeter; // calculate area
    let volume = area*height/3.0; // calculate volume of circumscribed polygon

    println!("The volume of the circumscribed polygon is {}", volume);
}
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This code first initializes the radius and height of the cone, as well as the number of sides in the circumscribed polygon. It then calculates the slant height, apothem, perimeter, area and volume of the circumscribed polygon using the formulas described above. Finally, it prints the result.