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

To find the volume of a regular polygon inscribed in a cylinder, we need to follow some steps:

1. Find the area of the base of the cylinder by taking its radius and squaring it, then multiplying by pi.
2. Find the height of the cylinder by dividing its volume by the area of the base.
3. Determine the apothem of the regular polygon by dividing the radius of the cylinder by the cosine of 180 degrees divided by the number of sides.
4. Find the perimeter of the regular polygon by multiplying the number of sides by the length of each side, which can be found using the radius and apothem.
5. Calculate the area of the regular polygon by multiplying the perimeter by the apothem and dividing by 2.
6. Multiply the area of the regular polygon by the height of the cylinder to get the volume.

Here's the implementation in TypeScript:

index.ts
function findVolumeOfRegularPolygonInscribedInCylinder(numSides: number, radius: number, height: number): number {
  const baseArea = Math.pow(radius, 2) * Math.PI;
  const volume = baseArea * height;
  const apothem = radius / Math.cos(180 / numSides);
  const perimeter = numSides * (2 * apothem * Math.tan(Math.PI / numSides));
  const area = (perimeter * apothem) / 2;
  return area * height;
}

// Usage example
const numSides = 6; // hexagon
const radius = 5;
const height = 10;
const volume = findVolumeOfRegularPolygonInscribedInCylinder(numSides, radius, height);
console.log(`Volume of hexagonal prism with radius ${radius} and height ${height}: ${volume}`);
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Note that the implementation assumes that the regular polygon is a prism (i.e., has the same height as the cylinder). If the height of the polygon is different from that of the cylinder, appropriate adjustments need to be made to the formula.