Archimedes' Buoyancy: Which Ball Will Experience a Greater Buoyant Force?

[Doc Al]

Ball A. Phrased wrong but imagine a flat plate. With larger surface area displaced when it's lying flat, it floats upwards. When tilted vertically it would sink.

What determines the buoyant force is not surface area, but volume of fluid displaced.

 

[insightful]

Ball A. Phrased wrong but imagine a flat plate. With larger surface area displaced when it's lying flat, it floats upwards. When tilted vertically it would sink.

Disregarding surface tension effects, your flat plate will either float (if less dense than water) or sink (if more dense than water) regardless of orientation.

 

[interestedcrl]

interested crl: I don't see dwg. details. But it gets more interesting if the bottom and sides of liquid container matches pretty well the contours of the object placed in it.
Then the liguid level rises surprising high fast, like a person's body in a bathtub, and theoretically a special body could then float on almost no 'weight' of water, and this makes a cute surprise joke for, say, a special solid wood cylinder in a special sized (nearly fitting) cup.