document.write( "Question 978174: You construct an open box from a square piece of material by cutting four centimeter squares from the corners and turning up the sides. The volume of the box is 576 cubic centimeters. Find the dimensions of the square piece of material that you used to construct the box. \n" ); document.write( "

Algebra.Com's Answer #599687 by KMST(5328) $\"\"$ $\"About$

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If the squares cut from the corners have sides measuring four centimeters,
\n" ); document.write( "the height of the box will be $\"4\"$ cm.
\n" ); document.write( "If the sides of the original square piece of material measured $\"x\"$ cm,
\n" ); document.write( "the bottom of the box will be a square with sides measuring $\"x-2%2A4=x-8\"$ cm.
\n" ); document.write( "

\n" ); document.write( "The surface area of the bottom (in square centimeters) will be $\"%28x-8%29%5E2\"$ ,
\n" ); document.write( "and that, multiplied times the height of the box in cm, $\"%284%29\"$ ,
\n" ); document.write( "is the volume in cubic centimeters:
\n" ); document.write( " $\"4%28x-8%29%5E2=576\"$
\n" ); document.write( "Solving:
\n" ); document.write( " $\"4%28x-8%29%5E2=576\"$
\n" ); document.write( " $\"4%28x-8%29%5E2%2F4=576%2F4\"$
\n" ); document.write( " $\"%28x-8%29%5E2=144\"$
\n" ); document.write( " $\"x-8=sqrt%28144%29\"$
\n" ); document.write( " $\"x-8=12\"$
\n" ); document.write( " $\"x=12%2B8\"$
\n" ); document.write( " $\"x=highlight%2820%29\"$ .
\n" ); document.write( "So the box was made from a square piece of material with sides measuring $\"highlight%2820cm%29\"$ . \n" ); document.write( "

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