Author: F. Huber
Date: 13:40:32 02/14/06
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On February 14, 2006 at 16:23:40, Dann Corbit wrote: >On February 14, 2006 at 14:25:08, F. Huber wrote: > >>On February 10, 2006 at 11:00:50, Derek Mauro wrote: >> >>>The questions were supposedly given in order of difficulty. I'll tell you the >>>other 2 questions and you can judge for yourself. >>> >>>Question 4: An inverted cone is filled with water. You are given 2 floating >>>point numbers: the radius and height of the cone. Find the radius of the sphere >>>which if dropped into the cone would have caused the maxiumum amount of water to >>>spill over the top. The answer has to be accurate to 3 significant digits. >> >>Here´s the solution for this puzzle: >> >>With R and H being the radius and height of the cone, and to shorten the >>solution >> >>k = sqrt((H/R)^2+1) - 1 >> >>the optimum radius (r) of the sphere is: >> >>r = H*(k+1) / (k*(k+3)) >> >>and the maximum amount (V) of water spilled over the top: >> >>V = 4*pi*H^3 / (3*k*(k+3)^2) >> >>Of course my interpretation of the text above is, that this sphere has NOT to be >>completely WITHIN the cone - otherwise there would be only one useful solution, >>but _this_ sphere would not displace the most water! > >An osmium ball 30 meters in diameter will spill more water. >;-) Not only water, but also the cone itself ... ;-)
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