find the volume of a regular polygon circumscribed around a sphere in javascript

To find the volume of a regular polygon circumscribed around a sphere, we need to know the radius of the sphere and the number of sides of the polygon.

Let's assume that the radius of the sphere is r and the number of sides of the regular polygon is n. We can use the following formula to calculate the volume of the polygon:

index.tsx
V = (0.25 * n * cos(pi/n) * sin(pi/n)^2 * r^3) / sin(pi/n)
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Here is the JavaScript code to perform this calculation:

index.tsx
function getVolumeOfPolygonCircumscribedAroundSphere(radius, numOfSides) {
  const pi = Math.PI;
  const cos = Math.cos;
  const sin = Math.sin;
  const volume = (0.25 * numOfSides * cos(pi/numOfSides) * Math.pow(sin(pi/numOfSides), 2) * Math.pow(radius, 3)) / sin(pi/numOfSides);
  return volume;
}

// example usage
const radius = 5;
const numOfSides = 8;
const volume = getVolumeOfPolygonCircumscribedAroundSphere(radius, numOfSides);
console.log(`Volume of a regular ${numOfSides}-sided polygon circumscribed around a sphere with radius ${radius} = ${volume}`);
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Hope this helps!

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