SOLUTION: given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long. What is the measure of a side (X) of a square to be cut from each corner in order to make the larges

Question 156413: given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long. What is the measure of a side (X) of a square to be cut from each corner in order to make the largest volume open top box.
Write the polynomial that represents volume.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
given a piece of rectangular cardboard that measures 15 cm wide and 29 cm long.
What is the measure of a side (X) of a square to be cut from each corner in
order to make the largest volume open top box.
:
Write the polynomial that represents volume.
:
The dimensions of the box will be;
(15-2x) by (29-2x) by x
:
FOIL the base:
(15-2x)* (29-2x) = 435 - 30x - 58x + 4x^2 which is: 4x^2 - 88x + 435
;
Multiply the base by the height (x)
(4x^2 - 88x + 435) * x = 4x^3 - 88x^2 + 435x
:
Vol = 4x^3 - 88x^2 + 435x
;
:
The easiest way to determine what value of x produces max vol, is to graph it:

You can see max occurs when x is a little over 3"
the trusty ti83 says 3.1467"
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