Author: Dann Corbit
Date: 13:23:40 02/14/06
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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. ;-)
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