document.write( "Question 548213: An open box is formed by cutting a 8 inch square measured from each corner and folding up the sides. If the volume of the carton is then 64 in3, what was the length of a side of the original square of cardboard? \n" ); document.write( "
Algebra.Com's Answer #357175 by KMST(5328)\"\" \"About 
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The original square of cardboard, with the cutting and folding lines would look like this:
\n" ); document.write( "Cutting lines are red, folding lines are blue.
\n" ); document.write( "You see 4 congruent squares cut out of the corners. If the length of the sides of those squares is 8 inches, then the height of the box will be 8 inches.
\n" ); document.write( "Let x be the length (in inches) of the side of the blue square (the bottom of the box).
\n" ); document.write( "The surface area of the bottom (in square inches) is \"x%5E2\",
\n" ); document.write( "and the volume of the box, calculated as area of the bottom times height, (in cubic inches) is
\n" ); document.write( "\"8x%5E2\"
\n" ); document.write( "So \"8x%5E2=64\" ---> \"x%5E2=64%2F8=8\" ---> \"x=sqrt%288%29=2sqrt%282%29\" or about 2.83 inches.
\n" ); document.write( "(That is going to be a tall box with a very narrow base, too easily tipped over.
\n" ); document.write( "I would have cut squares with side length 4 inches from the corner, and that would have given me a nice cube.)
\n" ); document.write( "So if the length of the side of the base is \"2sqrt%282%29\", with 8 inches of length added to each side, the length of the side of the original cardboard square must have been \"8%2B8%2B2sqrt%282%29=16%2B2sqrt%282%29\", or about 18.83 inches.
\n" ); document.write( "I still think we should have made a cubic box with 4 inch sides by cutting squares with 4 inch sides from a 12 inch by 12 inch square of cardboard. It would have used less material, wasted less material in the cutouts, for a box with the same volume, less surface, and much better stability. \n" ); document.write( "
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