The strength of a beam varies as the product of its breadth and square of its depth. Find the dimensions of the strongest beam which can be cut from a circular log of radius `adot`

Explanation

Let us assume `A B C D` be the cross section of beam that need to cut from the circular `log` of radius ' `a` '.

Let us assume 'b' be the depth of the rectangle, 'I' be the length of the rectangle and ' `d` ' be the diameter of circular log.

`Rightarrow d=2 a ldots ldots` (1)

According to the problem, strength of the beam is given by `Rightarrow {S}={lb}^{2} ldots ldots` (2)

From the `triangle {ABC}`,

`Rightarrow d^{2}=l^{2}+b^{2}`

From (1)


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