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

To find the volume of a regular polygon inscribed in a cone, we can use the formula:

V = (1/3) * B * h

where B is the area of the base of the cone, and h is the height of the cone.

The base of the cone is the regular polygon inscribed in it. To find the area of the base, we can use the formula:

B = (ap)/2

where a is the apothem (the perpendicular distance from the center of the polygon to the middle of any side) of the polygon, and p is the perimeter of the polygon.

To find the height of the cone, we can use trigonometry. Let r be the radius of the cone, and n be the number of sides of the inscribed polygon. Then, we know that the distance from the center of the polygon to any vertex is r, and the distance from the center of the polygon to the midpoint of any side is a. Therefore, we can draw a right triangle with hypotenuse r, one leg a, and the other leg h (the height of the cone).

Using Pythagorean theorem, we get:

h^2 = r^2 - a^2

To find the value of a, we can use the formula:

a = r * tan(pi/n)

where pi is the constant pi (approximately 3.14159), and n is the number of sides of the polygon.

Putting it all together, we get the following Rust function:

main.rs
fn inscribed_polygon_volume(r: f64, n: usize) -> f64 {
    let pi = std::f64::consts::PI;
    let a = r * (pi/n as f64).tan();
    let p = 2.0 * n as f64 * a;
    let b = (a * p)/2.0;
    let h = (r*r - a*a).sqrt();
    (1.0/3.0) * b * h
}
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Here, r is the radius of the cone, and n is the number of sides of the inscribed polygon. The function returns the volume of the inscribed polygon in the cone.