document.write( "Question 1194306: A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in. squares from each corner and folding up the sides. The box is to hold 6050 in3. How big a piece of cardboard is needed? \n" ); document.write( "

Algebra.Com's Answer #826474 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "A box with a square base and no top is to be made from a square piece of carboard
\n" ); document.write( "by cutting 2 in. squares from each corner and folding up the sides.
\n" ); document.write( "The box is to hold 6050 in3. How big a piece of cardboard is needed?
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document.write( "Let x be the side length (the dimension) of the square cardboard.\r\n" );
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document.write( "After cutting 2 in. squares at the corners of the cardboard and folding,\r\n" );
document.write( "the base of the box has dimensions  (x-4) inches by (x-4) inches.\r\n" );
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document.write( "The volume of the box is then  2*(x-4)^2, so we have this equation for x\r\n" );
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document.write( "    2*(x-4)^2 = 6050.\r\n" );
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document.write( "It implies\r\n" );
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document.write( "    (x-4)^2 = 6050/2 = 3025\r\n" );
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document.write( "     x-4    =  = 55 inches.\r\n" );
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document.write( "Hence,  x = 55 + 4 = 59 inches.\r\n" );
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document.write( "ANSWER.  The cardbox should be 59 x 59 inches.\r\n" );
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