Metasphere

Here is todays puzzle. If you think that you know the answer, please post it in the comments section.

Alfred has a metasphere. The metasphere is made of a blue material and a red material. At the center of the metasphere is a sphere of blue material that has a diameter of 1mm. That sphere is covered by a 1mm thick layer of red material. Then that sphere is covered by a 2mm thick layer of blue material. The layers keep increasing in thickness, with each layer being the thickness of the past 2 layers combined. There are 12 layers. The layers alternate red and blue materials. The blue material has a density of 1.7 grams/cubic centimeter. The red material has a density of 2.7 grams/cubic centimeter. What is the mass of the sphere? Please give your answer in grams and round to the nearest hundredth.

The answer will be posted on Tuesday.