- #1

ananonanunes

- 18

- 6

- Homework Statement
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- Relevant Equations
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I am given this expression which represents an object in 3D and the goal is to determine its volume using multiple integrals.

I started by drawing what I think is the object as well as two "slices" of that object on different planes (z=2 and z=1)

I have tried using cartesian, cylindrical and spherical coorddinates but I get a final result that seems impossible to integrate. My first instinct was to try to use Cavalieri's principle but I can't find a way to write the area of each "slice" only in terms of z. I think the problem is I'm not writing the limits of integration correctly so if anyone could help me out with that, it would be much appreciated.

(Final result is supposed to be 32/9)