SOLUTION: An open-top box with a square base is to be constructed from 120 square centimeters of material. What dimensions will produce a box a. of volume 100cm^3 b. with largest possible

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Question 864024: An open-top box with a square base is to be constructed from 120 square centimeters of material. What dimensions will produce a box
a. of volume 100cm^3
b. with largest possible volume?
Answers: a. approximately 4.427 inches by 4.427 inches
b The largest volume occurs when x= 10/3
*Please show work about this problem. I have been pondering about this question a lot. Thanks for your great help!


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x side of base
y height
120 square cm, amount of surface to make the box.

Surface area, 4%2Axy%2Bx%5E2=120.
Volume, v=yx%5E2.

(a):
To get v=100 cubic cms, try solving surface area equation for y and substitute into the volume equation.
S.A., 4xy=120-x%5E2
y=%28120-x%5E2%29%2F%284x%29
-
yx%5E2=100
%28%28120-x%5E2%29%2F%284x%29%29x%5E2=100
%28120-x%5E2%29x%2F4=100
%28120-x%5E2%29x=400
-x%5E3%2B120x-400=0
highlight%28x%5E3-120x%2B400=0%29
This gives x at 8.6 and 3.75, and you could check each of these for what happens to y using y=%28120-x%5E2%29%2F%284x%29. Graphing tool was used, and not polynomial property skills.