#!/usr/bin/env python
# coding=utf-8

"""449. Chocolate covered candy
https://projecteuler.net/problem=449

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  |  | π mm3  
---|---|---  
  
If a=2 mm and b=1 mm, the amount of chocolate required is approximately
60.35475635 mm

3

.

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.
"""
