elipsoid area function not giving correct results - php

Question

I have created a function to return the surface area of a given ellipsoid dimension but i am getting strange results.
Here is the function:
function elipsoid($a,$b,$c){
$ab=$a*$b;
$ab=pow($ab,1.6);
$ac=$a*$c;
$ac=pow($ac,1.6);
$bc=$b*$c;
$bc=pow($bc,1.6);
$abacbc=$ab+$ac+$bc;
$abacbc=$abacbc/3;
$prepie=pow($abacbc,0.016);
$fourpies=3.1415926535898*4;
$elipsoidarea=$prepie*$fourpies;
return $elipsoidarea;
}
If values of $a,$b,$c are all =1 the result is 12.566370614359 which according to the ellipsoid calculator on google is correct.
If values of $a,$b,$c are all =2 the result is 13.02034823541 which according to the ellipsoid calculator on google should be 50.26548.
I had my teenage daughter help translate this:
S≈4π((ab)1.6+(ac)1.6+(bc)1.63)1/1.6 (copy pasted from google hence doesn't look like the equation now lol).
Into "idiot" form such that I can understand it.
Is the calculation translation correct and/or have I coded it right? I also question how according to google a 4m wide sphere can have a surface area of 50m? Is Google wrong as well as the many sites that have this calculation option?

Answer 1

your doing wrong here,
$prepie = pow($abacbc,0.016);
It should be,
$prepie = pow($abacbc,0.625);
As of this,
root of 1.6 -> 1/1.6 -> 0.625