A machine produces open boxes using square sheets of metal. The machine cuts equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 256 cubic inches, find the length and width of the open box.

ANSWERS

2015-11-12 10:46:59

The original sheet is square shaped, with side length x. The dimensions of the box formed are (x-4) by (x-4) by 4. [latex]V_{box}=4(x-4)(x-4)\\256=4(x-4)(x-4)\\ frac{256}{4}=(x-4)^2\\ 64=(x-4)^2[/latex] thus x-4= 8 or x-4=-8. so x=12 or x=-4 which is clearly not considered. The length and the width of the box are x-4=12-4=8 (in) Answer: both are 8 in

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