Problem 449
Chocolate covered candy
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.
If a=1 mm and b=1 mm, the amount of chocolate required is $\frac{28}{3}$π 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.
巧克力糖衣
糖果师傅菲尔正在制造一种用巧克力做糖衣的新型糖果，每块糖的中心是一个椭球体，由如下方程给出：b2x2 + b2y2 + a2z2 = a2b2。
菲尔想知道，给这样一个糖果裹上一毫米厚的巧克力糖衣需要多少巧克力。
如果a=1 mm且b=1 mm，需要的巧克力是$\frac{28}{3}$π mm3。
如果a=2 mm且b=1 mm，需要的巧克力大概是60.35475635 mm3。
当a=3 mm且b=1 mm时，求需要多少巧克力（单位是mm3），并保留小数点后8位数字。