SOLUTION: Me. Greene has 8.5-by-11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to make an open-top box under these conditions: I)Each box must be made by

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Question 253379: Me. Greene has 8.5-by-11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to make an open-top box under these conditions:
I)Each box must be made by cutting small squares from each corner of a cardboard sheet.
II) The box must have a volume of 48 in^3
III) The amount of cardboard wast must be minimized.
What is the approxamite side length for the small squares that would be cut from the cardboard sheet?
A. 3.65 in
B. 2.66 in.
C. 0.71 in
D. 0.57 in
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = side of square to be cut.

volume of box will be:

(11-2x)*(8.5-2x)*x = 48

multiply out the factors to get:

4x^3 - 39x^2 + 93.5x = 48

substitute the values for x in each of the possible solutions to get:

selection a = 3.65 yielding y = 16.206
selection b = 2.66 yielding y = 48.045984
selection c = .71 yielding y = 48.156744
selection d = .57 yielding y = 41.364672

graph the equation y = 4x^3 - 39x^2 + 93.5x against the line y = 48 to see how this relates to the solutions.

graph+%28600%2C600%2C-10%2C10%2C-200%2C200%2C4x%5E3+-+39%2Ax%5E2+%2B+93.5x%2C48%29

you can see that there are 3 points where the graph of the equation intersect with y = 48.

those points are around .71, 2.66, and 6.something.

6.something was not one of the possible solutions.

.71 and 2.66 were.

the results show that both of these points are closer than the others with 2.66 being the closest.