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Multivariable CalculusHardTriple Integrals & Coordinate Systems

Triple Integrals & Coordinate Systems · Hard problem

A tank shaped like the paraboloid z=r2z=r^2 (in meters, r2=x2+y2r^2=x^2+y^2) is filled with water up to its rim at z=4z=4. To what depth hh (measured from the vertex at z=0z=0) would it need to be drained so that exactly half of the full volume of water remains?