The strength of a beam varies as the product of its breadth and square – InterviewSolution

InterviewSolution

1.	The strength of a beam varies as the product of its breadth and squareof its depth. Find the dimensions of the strongest beam which can be cut from a circular log of radius `adot`
Answer» `b^2/4+d^2/4=a^2` `d^2=4a^2-b^2` `(dS)/(db)=b(-2b)+(4a^2-b^2)` `=-2b^2+4a^2-b^2` `=4a^2-3b^2=0` `b^2=4/3a^2` `b=pm2/sqrt3` `d^2=4a^2-b^2` `=4a^2-4/3a^2` `d=2sqrt(2/3)a` `(d^2S)/(db^2)=-4b-2b` `=-6b<0` this will be maximum.

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