I think you will like the following problem PROBLEM 1244 of BERMAN's COLLECTION A log 20 m long is in the form of a frustum of a cone, the base diameters of which are 2 m and 1 m respectively. We want to cut out a beam from the log with a square cross- section and the same axes as the log, the volume of the beam being a MAXIMUM. What will be the dimensions of the beam ?
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