Problema Solution
The open tray shown in the illustration is to be manufactured from a 17-by-18-inch rectangular sheet of metal by cutting squares from each corner and folding up the sides. If the volume of the tray is to be 360 cubic inches and x is to be an integer, what size squares should be cut from each corner?
(L = 17 and w = 18 in the image below.)
in by
in
Answer provided by our tutors
The dimensions of the box are: 17 - 2x, 18 - 2x, and x
The volume of the box is: V = (17 - 2x)(18 - 2x)x
V = 360 in^3
(17 - 2x)(18 - 2x)x = 360
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click here to see the step by step solution for x
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one of the solution is x = 4
Indeed for x = 4 we have:
(17 - 2*4)(18 - 2*4)*4 = 9*10*4 = 360
The size of the squares that need to be cut have side lengths of 4 inches.