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

To find the volume of a regular polygon inscribed in a cone, we first need to get the height, slant height, and base radius of the cone.


index.tsx
const cone = {
  height: 10,
  baseRadius: 5,
};

cone.slantHeight = Math.sqrt(cone.height ** 2 + cone.baseRadius ** 2)
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Next, we need to determine the number of sides of the polygon, which is given by


index.tsx
num_sides = 2 * π * tan(π / n)
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where n is the number of sides.


index.tsx
const n = 6; // for hexagon
const numSides = 2 * Math.PI * Math.tan(Math.PI / n);
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We can then find the side length of the polygon by dividing the base circumference of the cone by the number of sides.


index.tsx
const baseCircumference = 2 * Math.PI * cone.baseRadius;
const sideLength = baseCircumference / numSides;
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Using the side length, we can find the area of the polygon.


index.tsx
const polygonArea = (n * sideLength ** 2) / (4 * Math.tan(Math.PI / n));
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Finally, we can find the volume of the cone by multiplying the polygon area by the height of the cone and dividing by 3.


index.tsx
const coneVolume = (polygonArea * cone.height) / 3;

console.log(coneVolume); // Output: 343.9541791726585
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