find the volume of a regular polygon circumscribed around a cone in typescript

index.ts
const radius = 5; // example value
const numSides = 6; // example value
const apothem = radius * Math.cos(Math.PI / numSides);
const slantHeight = Math.sqrt(radius ** 2 + apothem ** 2);
const height = slantHeight - radius;
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index.ts
const sideLength = 2 * radius * Math.sin(Math.PI / numSides);
const perimeter = sideLength * numSides;
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index.ts
const volume = (1 / 3) * Math.PI * radius ** 2 * height + (1 / 2) * perimeter * height;
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index.ts
function findVolumeOfRegularPolygonCircumscribedAroundCone(radius: number, numSides: number): number {
  const apothem = radius * Math.cos(Math.PI / numSides);
  const slantHeight = Math.sqrt(radius ** 2 + apothem ** 2);
  const height = slantHeight - radius;
  const sideLength = 2 * radius * Math.sin(Math.PI / numSides);
  const perimeter = sideLength * numSides;
  const volume = (1 / 3) * Math.PI * radius ** 2 * height + (1 / 2) * perimeter * height;
  return volume;
}
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