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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.
This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://numericalmethods.eng.usf.edu/videos.  Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.