Chocolate covered candy
Problem 449
Published on Sunday, 8th December 2013, 04:00 am; Solved by 451; Difficulty rating: 35%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: b^{2}x^{2} + b^{2}y^{2} + a^{2}z^{2} = a^{2}b^{2}.
Phil wants to know how much chocolate is needed to cover one candy centre with a uniform coat of chocolate one millimeter thick.
If a=1 mm and b=1 mm, the amount of chocolate required is 

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