Solution to Problem 103

Congratulations to this week's winner, Ray Kremer

Another correct solution was submitted by Andrew Hess. Correct solutions came from Philippe Fondanaiche, Burkart Venzke, Jens Voss, Ken Keating, Justin Crooks, Bryan Fluhrer, Khanh Ngo, Kimio Terauti, Jim Benstead, Ivan Lisac, Robert T McQuaid, Mark Foster, Russell Knight.

Ray Kremer's solution, presented here, is based on calculus, while Andrew Hess used only geometry. The sketch on the left shows a cross section of half of the submerged part of the cylinder, with h being the height of the water. The surface area of the cross section is given by the integral A =

and the submerged volume is 200A. This volume is added on top of the water already in the barrel, giving the equation 100²p(h-10) = 200A which can be solved numerically to give h = 10.44243161.

You are visitor number 4056 to this page.
Page last updated 1 December 2000.