Phil the confectioner is making a new batch of chocolate covered candy. Each candy centre is shaped like an ellipsoid of revolution defined by the equation: b²x² + b²y² + a²z² = a²b².

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

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.