find the volume of a regular polygon inscribed in a sphere in php

To find the volume of a regular polygon inscribed in a sphere, we need to use some geometry and math formulas. Here's the code in PHP:

main.php
<?php
function regular_polygon_volume($n, $r) {
    $pi = pi();
    $angle = 360/$n;
    $s = 2*$r*sin($pi/$n);
    $a = $r*cos($pi/$n);
    $b = sqrt(pow($r, 2) - pow($a, 2));
    $h = $b*sqrt(1 - pow(cos(deg2rad($angle/2)), 2));
    $area_base = 0.25*$n*$s*$a;
    $volume = (1/3)*$area_base*$h;
    return $volume;
}

// Example usage
$n = 6; // Number of sides of the regular polygon
$r = 10; // Radius of the sphere
$volume = regular_polygon_volume($n, $r);
echo "The volume of a regular polygon with $n sides inscribed in a sphere with radius $r is $volume";
?>
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In this code, we define a function regular_polygon_volume that takes two inputs: the number of sides of the regular polygon n and the radius of the sphere r. The function first calculates the side length s, the apothem a, the base length b, and the height h of the regular polygon using geometry formulas. It then calculates the area of the base and uses it to find the volume of the regular polygon using the formula volume = (1/3)*area_base*h. Finally, the function returns the volume.

In the example usage, we set n = 6 and r = 10, and then call the regular_polygon_volume function to find the volume of a regular hexagon inscribed in a sphere with radius 10. The result is printed to the console.