find the volume of a regular polygon circumscribed around a pyramid in csharp
To find the volume of a regular polygon circumscribed around a pyramid, we need to follow the below algorithm:
Calculate the surface area of the base of the pyramid (area of the regular polygon).
Find the apothem of the polygon, which is the distance from the center of the polygon to the midpoint of one of its sides.
Calculate the slant height of the pyramid, which is the distance from the center of the base polygon to the apex of the pyramid.
Calculate the volume of the pyramid using the formula: V = (1/3) * S * H, where S is the surface area of the base of pyramid and H is the height of the pyramid.
Return the volume of the pyramid.
Here is the C# code to implement the above algorithm:
main.cs
using System;
classProgram{
staticdoubleFindVolume(int n, double a, double h) {
// Calculate the surface area of the regular polygondouble area = (n * a * a) / (4 * Math.Tan(Math.PI / n));
// Find the apothem of the polygondouble apothem = (a / 2) * Math.Tan(Math.PI / n);
// Calculate the slant height of the pyramiddouble slantHeight = Math.Sqrt(Math.Pow(apothem, 2) + Math.Pow(h, 2));
// Calculate the volume of the pyramiddouble volume = (1.0 / 3) * area * h;
// Return the volume of the pyramidreturn volume;
}
staticvoidMain(string[] args) {
// Enter the number of sides of the polygon, the length of one side and the height of the pyramidint n = 4;
double a = 10;
double h = 20;
// Find the volume of the pyramiddouble volume = FindVolume(n, a, h);
// Display the volume of the pyramid Console.WriteLine("Volume of the pyramid = " + volume);
Console.ReadKey();
}
}