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we have to consider that the bottle is actually 3D and the bottle has a long axis that is a vertical line through O. if you slice horizontally, you get circle cross-sections. if you slice diagonally, how do you get a hemisphere + (triangle/ pyramid/ cone?) with semicircle base?
I believe the correct way is to slice the top cap off horizontally along EF, then move this cap to the bottom to form a complete hemisphere. above XY, you are just left with a cylinder with radius OX and height XE.
by calculation, ...
volume of cylinder
= pi x r2 x h
= 71.086127
volume of hemisphere
= (1/2) x (4/3) x pi x r3
= 134.0412866
giving total volume = 205 cm3.
(amazingly, Eugene's method gives the same volumes for the 2 portions even though the shapes are hard to comprehend).