In this task you have to find the volume of T, and in the proposed solution you find it by symmetry and double integral. They find that theta should be between 0 and 3*pi/2, which I don't quite understand. The solution for the volume should be equal to 32*pi/9. I still don't understand how to solve this problem. Could you try to solve the task and explain in detail what you are doing step by step?

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Let T be the area in space given by

3x2 - y= = 0. X 20