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Do you know ? You asked a tough question.
Is this your assignment/home work or you are asking it for someone else?
This is a difficult question because it involves so many things like
Integration, curves and then volume of rotating region.
One more thing "Annulus".
There are only two points of intersection of this region (0,0) and (1,1).
To explain this level of Maths is so difficult because when region rotated it will generate some solid. I suggest you to use paper and draw a graph. It will help you.I am sorry I am not very helpfull. There is a solution in my mind , I am not sure it is right.
If I will find out I will send you.
Maths question...Volume of Revolution :o( 
Linear Mode
