Problema Solution
An open box is to be constructed from a square piece of sheet metal by removing a square side 6 feet from each corner and turning up the edges. If the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?
Answer provided by our tutors
let
a = the length of the side of the square piece of metal, a>0
the dimensions of the box will be:
width = a - 2*6 = a - 12 ft
length = a - 2*6 = a - 12 ft
height = 6 ft
the volume of the box V = width*length*height
(a - 12)(a - 12)*6 = 864
by solving we find
a = 24 ft
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the length of the side of the square piece of metal sheet is 24 feet.