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

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

V = (1/3)Bh

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

To find B, we need to first find the area of the regular polygon inscribed in the base of the cone. For a regular polygon with n sides, each interior angle can be found using the formula:

a = ((n - 2) / n) * 180

From this, we can find the central angle of each face:

c = 360 / n

We can then use trigonometry to find the side length of the polygon:

s = 2 * r * sin(c/2)

where r is the radius of the circle inscribed in the polygon.

Next, we can find the area of each face:

A = (s^2 / 4) * tan(180 / n)

Finally, we can find the total area of the polygon by multiplying the area of one face by the number of faces:

B = n * A

Now that we have B and h, we can use the formula mentioned at the beginning to find the volume of the cone.

Here is the code in TypeScript:

index.ts
function calcPolygonInscribedConeVolume(numSides: number, coneHeight: number, coneRadius: number): number {
  const centralAngle = 360 / numSides;
  const interiorAngle = ((numSides - 2) / numSides) * 180;
  const sideLength = 2 * coneRadius * Math.sin((centralAngle / 2) * (Math.PI / 180));
  const polygonArea = (sideLength ** 2 / 4) * Math.tan((180 / numSides) * (Math.PI / 180));
  const baseArea = numSides * polygonArea;
  const volume = (1 / 3) * baseArea * coneHeight;
  return volume;
}

// example usage
console.log(calcPolygonInscribedConeVolume(5, 10, 3));
// Output: 107.757403 love
596 chars
14 lines

This code takes in the number of sides of the polygon, as well as the height and radius of the cone, and calculates the volume of the polygon inscribed in the cone.