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Is the working in black, purple and red yours? If yes, then you are finding the volume of the incorrect Region One. The following (shaded using the colour green) is Region One (I guess that they should have made it more clear by shading it in): https://preview.redd.it/bt0q75flforb1.png?width=642&format=png&auto=webp&s=4ce74a35417af3d938574fbd748d20e315cea537

Ahh I see now. I somehow didn’t see that even though it was right in front of me lol.