Question 1156438
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<pre>

Let x be the original side measure of the square piece of cardboard.


After cutting 2 inch squares in each angle and folding sides up, the square base has the dimensions (x-2) inches.


So, the volume of the box is then  V = 2*(x-4)*(x-4).


So, you have this equation


    {{{2*(x-4)^2}}} = 162.


From the equation,


    {{{(x-4)^2}}} = 162/2 = 81,   x-4 = {{{sqrt(81)}}} = 9,  x = 9 + 4 = 13.


<U>ANSWER</U>.  The original piece was 13 inches square cardboard.
</pre>

Solved.


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If you want to see many other similar solved problems, look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Making-a-box-from-a-piece-of-cardboard.lesson>Making a box from a piece of cardboard</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Dimensions and the area of rectangles and circles and their elements</U>".


Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.