Here is another Wolfram demo. This one shows how much of a floating ball would be submerged under water. The demonstration uses the specific gravity and radius of the ball as inputs. Using calculus and Archimedes’ principle, the level to which the ball is submerged turns out to be the solution of a cubic equation. To play with the demo, download the free CDF player from Wolfram first.
The demo is at http://demonstrations.wolfram.com/FloatingBall/
Reference: Floating Ball Derivation
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