Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · hard
The strength of a rectangular beam varies as the product of its width and the square of its depth. Find the width of the strongest beam that can be cut from a circular log of diameter 20 cm.
- 11.55 cm
- 10.00 cm
- 6.67 cm
- 14.14 cm
Answer
A. 11.55 cm
Solution
Width w and depth d satisfy w2+d2=400 (the diagonal equals the log's diameter). Strength S=kwd2=kw(400-w2). S'=k(400-3w2)=0 w2=400/3 w=20/ 3 11.55 cm.
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