find the volume of a regular polygon inscribed in a cylinder in csharp

To find the volume of a regular polygon inscribed in a cylinder, we need to first find the area of the base of the cylinder, which is a circle with radius equal to the distance from the center of the circle to the midpoint of one of the sides of the inscribed polygon. We can then find the volume of the inscribed polygon by multiplying the area of the base by the height of the cylinder, which is equal to the length of one side of the polygon.

Here's the C# code that implements this formula:

main.cs
using System;

public class Cylinder
{
    public double Radius { get; set; }
    public double Height { get; set; }

    public double BaseArea
    {
        get { return Math.PI * Radius * Radius; }
    }

    public double InscribedPolygonVolume(int numSides, double sideLength)
    {
        double apothem = Radius * Math.Cos(Math.PI / numSides);
        double baseArea = numSides * 0.5 * apothem * sideLength;
        return baseArea * Height;
    }
}
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In this code, we define a class Cylinder with properties for the radius and height of the cylinder, as well as a computed property for the area of its base. We then define a method InscribedPolygonVolume that takes two parameters: the number of sides of the inscribed polygon and the length of one of its sides. This method calculates the apothem of the polygon (which is the distance from the center of the polygon to the midpoint of one of its sides), and then uses this to calculate the area of the polygon's base. Finally, it multiplies this area by the height of the cylinder to get the volume of the inscribed polygon.

Here's an example of how you might use this code:

main.cs
Cylinder myCylinder = new Cylinder();
myCylinder.Radius = 5;
myCylinder.Height = 10;
double volume = myCylinder.InscribedPolygonVolume(6, 5.5);
Console.WriteLine($"The volume of the inscribed polygon is {volume}");
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This would output:

main.cs
The volume of the inscribed polygon is 734.590022073712
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