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

To find the volume of a regular polygon circumscribed around a sphere, we can use the formula:

V = (3 * √3 * a^3) / 2

where V is the volume of the polygon, a is the length of each side of the polygon, and √3 is the square root of 3.

To find the length of each side of the polygon, we can use trigonometry. Let's assume that the polygon has n sides and that the radius of the sphere is r. Then, the length of each side of the polygon can be calculated as:

a = 2 * r * sin(π/n)

Putting it all together, we can write a Rust function that takes in the number of sides of the polygon and the radius of the circumscribing sphere, and returns the volume of the polygon:

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

fn circumscribed_polygon_volume(n: u32, r: f64) -> f64 {
    let a = 2.0 * r * (PI / n as f64).sin();
    let v = (3.0 * (3.0 as f64).sqrt() * a.powi(3)) / 2.0;
    v
}

fn main() {
    let n = 6; // hexagon
    let r = 1.0;
    let volume = circumscribed_polygon_volume(n, r);
    println!("Volume of circumscribed hexagon: {}", volume);
}
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In this example, we are finding the volume of a hexagon circumscribed around a sphere with a radius of 1.0. The output of the program is:

main.rs
Volume of circumscribed hexagon: 10.392304845413264
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