This roughly checks out. I’m getting 66%, based on the methodology of cutting out the jug’s shape from the picture and numerically integrating the filled and empty volume (e.g. if a row is d pixels wide, it contributes d^2 to the volume, either filled or empty depending on whether it’s above or below the water level).
The thing I said I did? Yes; here’s the processed image:
If you mean the math in the post, I can’t read it in this picture but it’s probably just some boring body-of-rotation-related integrals, so basically the same thing as I did but breaking apart the vase’s visible shape into analytically simple parts, whereas I got the shape from the image directly.