Problema Solution
An open box is to be constructed from a square piece of sheet metal by removing a square of 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
x = the length of the square piece of sheet metal
x - 2*6 = x - 12 the length of the sides of the box, x > 12
h = 6 ft the height of the box
V = 864 ft^3 the volume of the box
V = h(x - 12)^2
V = 6(x - 12)^2
Now we can write
9(x - 8)^2 = 72
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x = 10.83 ft
The dimensions of the square sheet metal is 10.83 feet approximately.