double integral 問題

I think the question clear. x^2+y^2=16 only refers to the shell. If it refers to the solid,the equation should be x^2+y^2 <=16. Likewise for x^2 + y^2 + z^2 = 64

2012-11-16 19:47:15 補充：
So the cylinder is a knife that cut into the spherical shell and divide the surface areas into 2 parts. The cylindrical wall belongs to x^2+y^2=16, not the spherical shell. So the question is asking for the ratio of areas on the spherical shell

2012-11-16 19:48:56 補充：
AS 翻雷滾天 風卷殘雲 has said, the surface areas can be calculated without using double integral. But for practicing purpose, we can still use double integral to do it.

2012-11-16 19:49:14 補充：
Please see my solution:
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1841.png

2012-11-16 21:51:41 補充：
Look at this:
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1007.png

2012-11-17 08:10:08 補充：
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圖片參考：http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-1841.png

If just finding the surface area, it may not be involving double integral

In fact I'm confused about the question...
Where are the areas of A(I) and A(O)?
Do they include the side area of the cylinder?
Or it just (incredibly) want us to compare the volume of I and O?

2012-11-16 12:43:44 補充：
Even if the side area of the cylinder is included, double integral is not necessary.
If this is a question about volume, it is a simple multiple integral question.

2012-11-17 05:36:21 補充：
Oops.
It seems that I was stuck at the wordings stupidly xD
Thanks for 自由自在 to explain clearly.