--description--

Phil the confectioner is making a new batch of chocolate covered candy. Each candy center is shaped like an ellipsoid of revolution defined by the equation: $b^2x^2 + b^2y^2 + a^2z^2 = a^2b^2$.

Phil wants to know how much chocolate is needed to cover one candy center with a uniform coat of chocolate one millimeter thick.

If $a = 1$ mm and $b = 1$ mm, the amount of chocolate required is $\frac{28}{3} \pi$ mm³

If $a = 2$ mm and $b = 1$ mm, the amount of chocolate required is approximately 60.35475635 mm³.

Find the amount of chocolate in mm³ required if $a = 3$ mm and $b = 1$ mm. Give your answer as the number rounded to 8 decimal places behind the decimal point.

--hints--

chocolateCoveredCandy() should return 103.37870096.

assert.strictEqual(chocolateCoveredCandy(), 103.37870096);

--seed--

--seed-contents--

function chocolateCoveredCandy() {

  return true;
}

chocolateCoveredCandy();

--solutions--

// solution required