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

Question 198713: Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to amke 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 waste must be minimized.
What is the appropriate side length for the small squares that would be cut from the cardboard sheet?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mr. Greene has 8.5 in 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.
Let the side of the small square = x
then
the dimension of the box: (8.5-2x) by (11-2x) by x
FOIL
x(93.5 - 17x - 22x +4x^2)
A volume equation
V = 4x^3 - 39x^2 + 93.5x
:
;
II. The box must have a volume of 48 in^3
4x^3 - 39x^2 + 93.5x = 48
4x^3 - 39x^2 + 93.5x - 48 = 0
:
:
III. The amount of cardboard waste must be minimized.
Graph the above equation to find the values of x:

What is the appropriate side length for the small squares that would be
cut from the cardboard sheet?
:
The smaller solution: x ~.7"; would give us the smallest removed squares
;
;
:
Check our solution: 2x = 1.4
(8.5-1.4) * (11-1.4) * .7 =
7.1 * 9.6 * .7 = 47.4 ~ 48
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